Answer:
The hang time is 0.63 seconds
Step-by-step explanation:
We want to find out what the cricket's fall time is and we have the function that describes its height as a function of time.
The cricket is on the ground when its height is equal to zero. Therefore we must equal h to zero and solve the equation for t ..
[tex]h=-16t^2+10t\\\\-16t^2 +10t=0\\\\\\[/tex]
We take t as a common factor
[tex]-16t^2 +10t=0\\\\t(10-16t)=0[/tex]
Then the height is zero when t = 0 and when (10-16t) = 0
[tex]t=0[/tex]
[tex]10-16t= 0[/tex]
[tex]10 = 16t[/tex]
[tex]t=\frac{10}{16}\\\\t= 0.63\ sec[/tex]
At t = 0 seconds the cricket is still on the ground.
Then the cricket is in the air and after 0.63 seconds the cricket falls back to the ground
Complete the square:
[tex]-16t^2+10t=-16\left(t^2-\dfrac58t\right)=-16\left(t^2-\dfrac58t+\dfrac{25}{256}-\dfrac{25}{256}\right)=-16\left(t-\dfrac5{16}\right)^2+\dfrac{25}{16}[/tex]
That is, [tex]h(t)[/tex] has a maximum value of [tex]\dfrac{25}{16}\approx1.6[/tex] ft when [tex]t=\dfrac5{16}\approx0.3[/tex] s. It takes the cricket twice as much time to jump up to its maximum height and return to the ground, so that the hang time is about 0.6 s.
what is 2+5 nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Answer:
7
Step-by-step explanation:
2 + 5=7
The answer is 7 duhhhhhh
*** PLS HELP ASAP (14 points)
two triangles were required to construct the figure below.
what is the sum of the measures of the interior angles of this figure?
1. 136°
2. 272°
3. 360°
4. 720°
Answer:
Option 3. 360°
Step-by-step explanation:
we know that
The sum of the measures of the interior angles of triangle is equal to 180 degrees
The figure has two triangles
therefore
[tex]2(180\°)=360\°[/tex]
Alternative Method
The formula to calculate the sum of the measures of the interior angles of a polygon is equal to
[tex]S=180(n-2)[/tex]
where
n is the number of sides of the polygon
In this problem we have a a quadrilateral
so
n=4
substitute
[tex]S=180(4-2)[/tex]
[tex]S=180(2)[/tex]
[tex]S=360\°[/tex]
Answer:
360
Step-by-step explanation:
Solve for x x squared plus 4X minus 21 equals 0
Answer:
x = -7 and x = 3
Step-by-step explanation:
x² + 4x - 21 = 0 factors as follows: (x + 7)(x - 3) = 0.
Then x = -7 and x = 3.
Answer:
[tex]x = 3\\x = -7[/tex]
Step-by-step explanation:
We have the following quadratic equation
[tex]x^2 + 4x - 21 =0[/tex]
To solve the equation we must factor it.
To factor the equation we must find 2 numbers b and c that when adding them, you obtain as result 4 ([tex]c + b = 4[/tex]) and when multiplying them, you obtain as result -21 ([tex]c * b = -21[/tex]).
Then the polynomial will be factored in the following way:
[tex](x+c)(x + b) = 0[/tex]
You can verify that the numbers that meet this condition are:[tex]b = 7\\c = -3[/tex]
So
[tex]x^2 + 4x - 21 =(x-3)(x + 7)=0[/tex]
Finally the solutions are:
[tex]x = 3\\x = -7[/tex]
Choose the algebraic expression for x times 8 is equal to 11
A- x+8=11
B- 8x=11
C- x/8=11
D- x-8=11
It’s B
X•8 it the same as 8x
Help?! “Find the area of each figure. Round your answer the nearest tenth”
Answer:
Check attached graph
Step-by-step explanation:
Given equation is .
Now we need to graph the given equation .
To graph that we can find two points then join them by a straight line.
We are free to plug any number for x say x=0 and x=2
plug x=0
Hence first point is (0,-2).
plug x=2
Hence first point is (2,0).
Now graph both points and joint them to get final graph as shown below.
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The time required to finish a test in normally distributed with a mean of 40 minutes
and a standard deviation of 8 minutes. What is the probability that a student chosen
at random will finish the test in less than 48 minutes?
84%
2%
34%
16%
Answer:
84%.
Step-by-step explanation:
Let X be the time in minutes for a student chosen at random to finish the test. [tex]X\sim N(40, 8^{2})[/tex].
The probability that a student chosen at random finishes the test in less than 48 minutes will represented as
[tex]P(X< 48)[/tex].
Method 1: technologyEvaluate the cumulative normal probability on a calculator, where
The lower bound is 0,The upper bound is 48, The mean [tex]\mu = 40[/tex],The standard deviation [tex]\sigma = 8[/tex][tex]P(X < 48) = 0.8413[/tex].
Method 2: z-score table[tex]x = 48[/tex].
[tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{48 - 40}{8} = 1[/tex].
Look up the entry that corresponds to [tex]z = 1.000[/tex] on a z-score table: 0.8413.
In other words,
[tex]P(X < 48) = P(Z < 1) = 0.8413[/tex].
The Z-score for 48 minutes is 1, corresponding to a cumulative probability of approximately 84%.
Calculating Probability for Normally Distributed Data
The time required to finish a test is normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. We need to find the probability that a student chosen at random will finish the test in less than 48 minutes.
First, calculate the Z-score using the formula:Z = (X - μ) / σ
where X is the value of interest (48 minutes), μ is the mean (40 minutes), and σ is the standard deviation (8 minutes). This gives us:
Z = (48 - 40) ÷ 8 = 1
2. Next, use the Z-score to find the probability from the standard normal distribution table. A Z-score of 1 corresponds to a probability of approximately 0.8413 or 84.13%.
Therefore, the probability that a student chosen at random will finish the test in less than 48 minutes is 84%.
What is the value of X?
A) 20
B) 35
C) 60
D) 70
Answer:
x = 20
Step-by-step explanation:
When two lines intersect they form two pairs of opposite angles which are also known as vertical angles. Vertical angles are always congruent which means that they are equal.
Angle TRS = Angle VRW
x + 40 = 3x
x - x + 40 = 3x - x
40 = 2x
40/2 = 2x/2
20 = x
(20 + 40) = 3(20)
60 = 60
Answer:
x = 20
Step-by-step explanation:
The given angles are vertical and congruent, so
3x = x + 40 ( subtract x from both sides )
2x = 40 ( divide both sides by 2 )
x = 20
A band selects 404040 ticket-holders at random from each concert to win t-shirts. The band knows that 55\%55%55, percent of the ticket-holders buy their tickets at least a month before the concert. Suppose the band calculated the proportion \hat p
p
^
of winners from each concert who bought their tickets at least a month before the concert.
Which of the following distributions is the best approximation of the sampling distribution of \hat p
p
^
?
Each distribution uses the same scale.
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
(Choice B)
B
(Choice C)
C
(Choice D)
D
Answer:
They would be normally distributed.
Step-by-step explanation:
Because there are more than 30 samples, the distribution would closely resemble the normal distribution.
40 ticketholders are winning the contest. 40 ≥ 30. This is enough to make the distribution approximately normal.
Based on the information given regarding the sampling distribution, the approximation would be normally distributed.
What is Sampling distribution?It should be noted that sampling distribution simply means a probability distribution of a statistic obtained from a larger number of samples that are drawn.
In this case, since there are more than 30 samples, the distribution would closely resemble the normal distribution. Therefore, this makes the distribution approximately normal.
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Rewrite the expression with rational exponents as a radical expression.
Answer:
[tex]7\sqrt[3]{x^2}[/tex]
Step-by-step explanation:
The rule of exponents that dictates this to be solved is:
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]
The power of 2/3 is on "x", NOT 7, so we use this property to write it as:
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a} \\7x^{\frac{2}{3}}=7\sqrt[3]{x^2}[/tex]
third answer choice is right, [tex]7\sqrt[3]{x^2}[/tex]
Answer:
b or the second one top to botton
Step-by-step explanation:
trust
what percent of 60 is 27?
22 is 55% of what?
For this question, set up an equation. 60 times what decimal is 27?
60x=60
x=0.45
Convert this decimal to a percentage by multiplying it by 100:
45%
For this question, set up an equation. 55% (or 0.55) times what number equals 22?
0.55x=22
*Divide both sides by 0.55*
x=40
Hope this helps!!
Regan used 1,332 sq ft of wrapping paper to wrap gifts for everyone in her class. If each gift used the same amount of wrapping paper and she wrapped 24 gifts, how much wrapping paper did she use for each gift?
Answer:
The answer is 55.5 sq ft per gift.
Step-by-step explanation:
1,332 square feet in all.
If there is 24 gifts then you divide 1,332 by 24.
1,332 divided by 24 is 55.5.
I hope this helps. :)
Final answer:
Regan used 55.5 square feet of wrapping paper for each gift after dividing the total square feet of wrapping paper by the number of gifts.
Explanation:
Regan wrapped 24 gifts using 1,332 square feet of wrapping paper in total. To find out how much wrapping paper she used for each gift, we need to divide the total square feet of wrapping paper by the number of gifts.
The calculation would be 1,332 sq ft ÷ 24 gifts = 55.5 sq ft per gift. Therefore, Regan used 55.5 square feet of wrapping paper for each gift.
3 The Hawks soccer team played a total of 24 games. They won 6 more games than they lost, and they tied 2 games. How many games did they win?
They won 14 games. If you subtract 2 ( the ties ) you are left with 22. Subtract 6 ( games more won than loss) you get 16. Then divide by two and get 8. 8 + 6 = 14.
Answer:
14 games.
Step-by-step explanation:
Let x represent number of games lost by Hawks.
We have been given that the Hawks won 6 more games than they lost. So number of games won by Hawks would be [tex]x+6[/tex].
We have been given that they played a total of 24 games and tied in 2 games, so total game won or lost by Hawks would be [tex]24-2=22[/tex].
Now we will equate sum of games won and lost by 22 as:
[tex]x+x+6=22[/tex]
[tex]2x+6=22[/tex]
[tex]2x+6-6=22-6[/tex]
[tex]2x=16[/tex]
[tex]\frac{2x}{2}=\frac{16}{2}[/tex]
[tex]x=8[/tex]
Number of games won by Hawks would be [tex]x+6\Rightarrow 8+6=14[/tex]
Therefore, Hawks won 14 games.
What is the solution of
Answer:
Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]
correct choice is B because both ends are open circles.
Step-by-step explanation:
Given inequality is [tex]\frac{x+8}{5x-1}>0[/tex]
Setting both numerator and denominator =0 gives:
x+8=0, 5x-1=0
or x=-8, 5x=1
or x=-8, x=1/5
Using these critical points, we can divide number line into three sets:
[tex](-\infty,-8)[/tex], [tex]\left(-8,\frac{1}{5}\right)[/tex] and [tex](\frac{1}{5},\infty)[/tex]
We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.
Test for [tex](-\infty,-8)[/tex].
Clearly x=-9 belongs to [tex](-\infty,-8)[/tex] interval then plug x=-9 into [tex]\frac{x+8}{5x-1}>0[/tex]
[tex]\frac{-9+8}{5(-9)-1}>0[/tex]
[tex]\frac{-1}{-46}>0[/tex]
[tex]\frac{1}{46}>0[/tex]
Which is TRUE.
Hence [tex](-\infty,-8)[/tex] belongs to the answer.
Similarly testing other intervals, we get that only [tex](-\infty,-8)[/tex] and [tex](\frac{1}{5},\infty)[/tex] satisfies the original inequality.
Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]
correct choice is B because both ends are open circles.
Answer:
[tex]x \:<\:-8[/tex] or [tex]x \:>\:\frac{1}{5}[/tex].
Step-by-step explanation:
The given inequality is [tex]\frac{x+8}{5x-1} \:>\:0[/tex]
For this statement to be true, then we must have the following cases:
Case 1
[tex]x+8 \:<\:0\:and\:5x-1\:<\:0[/tex]
[tex]x \:<\:-8\:and\:x\:<\:\frac{1}{5}[/tex]
The intersection of these two inequalities is [tex]x \:<\:-8[/tex].
The solution to this first case is [tex]x \:<\:-8[/tex].
Case 2
[tex]x+8 \:>\:0\:and\:5x-1\:>\:0[/tex]
[tex]x \:>\:-8\:and\:x\:>\:\frac{1}{5}[/tex]
The intersection of these two inequalities is [tex]x \:>\:\frac{1}{5}[/tex].
The solution to this second case is [tex]x \:>\:\frac{1}{5}[/tex].
Therefore the solution to the given inequality is
[tex]x \:<\:-8[/tex] or [tex]x \:>\:\frac{1}{5}[/tex].
The second option is correct
The price for a pair of sandals is $49.95 in June. In August the price is 60% less. Which expression gives the price of the sandals in August?
To calculate the new discounted price, $49.95×.60=$29.97
Answer:
The required expression is [tex]0.40\times 49.95[/tex].
Step-by-step explanation:
Consider the provided information.
The price for a pair of sandals is $49.95 in June.
In August the price is 60% less.
After getting 60% discount customer need to pay only 40% of the price.
This can be written as:
[tex]40\% \times 49.95[/tex]
[tex]\frac{40}{100}\times 49.95[/tex]
[tex]0.40\times 49.95[/tex]
Hence, the required expression is [tex]0.40\times 49.95[/tex].
Write an equation for each problem. The square of a number is 8 more than twice the number.
Answer:
The equation is equal to
[tex]x^{2}=2x+8[/tex]
Step-by-step explanation:
Let
x -----> the number
we know that
The equation that represented the problem is equal to
[tex]x^{2}=2x+8[/tex]
[tex]x^{2}-2x-8=0[/tex]
Solve the quadratic equation by graphing
The solution are x=-2 and x=4
see the attached figure
therefore
The number can be -2 or 4
Select all the words that mean exponential growth
-increase
-decay
-decrease
-appreciate
-rise
-lower
-depreciate
Answer:
increase, appreciate, rise
Step-by-step explanation:
The words associated with expo GROWTH are
increase, appreciate, rise.
All the others are often but not always associated with expo DECAY.
Answer:
increase
rise
appreciate
They a;ll mean increase:)
Mark Brainlyest please
One delivery driver can complete a route in 7 h another can do the same route in 11 hours. What equation can the drivers use to determine time T in hours needed to complete the route when they work together?
The equation that the drivers use to determine the time is (1/7)n + (1/11)n.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Here, we have
Given: One delivery driver can complete a route in 7 h another can do the same route in 11 hours.
We have to determine the equation can the drivers use to determine time T in hours needed to complete the route when they work together.
We concluded that
= (1/7)n + (1/11)n
Hence, the equation that the drivers use to determine the time is (1/7)n + (1/11)n.
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Twenty of the two dozen members voted yes. What fraction of the members voted yes?
Answer:20/24
Step-by-step explanation:
To find the fraction of members that voted yes, we need to divide the number of members that voted yes by the total number of members.
Given:
- Total number of members (two dozen): 1 dozen is 12 members, so two dozen is 2 x 12 = 24 members.
- Number of members that voted 'yes': 20 members.
Now, to find the required fraction, we perform the following division:
Fraction of members that voted yes = (Number of members that voted 'yes') / (Total number of members)
= 20 / 24
This fraction can be simplified to its lowest terms by dividing both the numerator (20) and the denominator (24) by their greatest common divisor (GCD), which is 4:
Simplified fraction = (20 ÷ 4) / (24 ÷ 4)
= 5 / 6
Therefore, the fraction of members that voted yes is 5/6.
An 80 kg Rottweiler needs 40 mL/kg over 12 hours. What's the flow rate per hour? A. 267 mL/hr B. 3,200 mL/hr C. 3.3 mL/hr D. 133 mL/hr
Answer:
A
Step-by-step explanation:
40ml/kg
Kg are 80 so i multiply 40×80 and I get 3200Ml, that is the amount of watet the rottwailer needs in 12 hours. But, because i need to find the amount in 1 hour i do 3200/12 and i get 266,666666 that i approximate to 267.
The flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.
What is the flow rate per hour of the given sample ?It is given that the 80 kg Rottweiler needs 40 mL/kg over 12 hours.
Therefore, the flow rate per hour can be found out just by comparing the units and dimensions of the given sample with the required sample to found out.
The flow rate per hour is -
= ( 80 kg ) * (40 mL/kg) * (1/12 hours)
= (80 * 40) / 12 mL/Hours
= 266.6667 mL/hr
≈ 267 mL/hr .
Thus, the flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.
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A cab company offers a special discount on fare to senior citizens. The following expression models the average amount a cab driver of the company collects on a particular day, where x represents the number of senior citizens who travel by the company's cabs.
What does the constant term in the above expression represent?
help right away picture is attached
Answer:
D. The constant 250 represents the average collection when no seniors ride.
Step-by-step explanation:
A -- the entire expression represents the driver's pay, not just the constant 250.
B -- collections continue to increase as x goes up, so 250 is the minimum, not the maximum.
C -- x is the number of seniors; 250 is in units of collections (dollars?), not numbers of seniors.
D -- indeed, 250 is the "y-intercept" of the expression, hence the collection when no seniors ride.
PLEASE HELP! 15 POINTS! HELP ASAP! Will give brainlist
The question is down below is the photo. If you help you will save my life. Thank you tons!
50 miles per hour
80.5 km per hour
80,467 meters per hour
4,828,032 meters per minute
Hope this helps!! :)
What they said ^^^^^^^^^^^^^^^
please help. please
Answer:
B
Step-by-step explanation:
In the right triangle with hypotenuse of 10 use the sine ratio to find x
sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]
Multiply both sides by 10
10 × sin20° = x, hence
x ≈ 3.4 ( to the nearest tenth ) → B
Test 43,785 for divisibility by 2, 3, 5, 9, and 10.
43785 is not divisible by 2 because it's not an even number, and this also means it's not divisible by 10 because 10 = 2*5.
The sum of its digits is 4 + 3 + 7 + 8 + 5 = 27, which is divisible by 3 since 27 = 3*9, so 43785 is divisible by 3. We have 43785 = 3*14595.
It would be divisible by 9 if 14595 were also divisible by 3. That number has digital sum 1 + 4 + 5 + 9 + 5 = 24, which is divisible by 3, so 14595 is too and 14595 = 3*4865. So 43785 = 9*4865, and it is indeed divisible by 9.
14595 is clearly divisible by 5 because its ends with a 5.
Given O below, the arcs AB and CD must be congruent.
Answer:
Option A true is the answer.
Step-by-step explanation:
The given circle there are two arcs AB and CD.
Angles formed by these arcs at the center arc 30°
Formula of length of arc = r × θ
where r = radius of the circle
and θ = angle formed by arc at the center.
mAB = OA × (30°) [ By formula ]
similarly mCD = DC × (30°)
Since OA = OC = r (radii of the circle )
So mAB = mCD
Therefore, statement is true.
Option A true is the answer.
Answer:true
Step-by-step explanation:
Which is the principal of value of arctan (2.6) ?
Answer:
arctan(2.6) = 68.96
Step-by-step explanation:
To find the arctan of 2.6, we are going to use calculator:
Then, we have that arctan(2.6) = 68.96.
The principal value of arctan(2.6) is 1.231 radians or approximately [tex]70.43^o[/tex].
The arctan function, also known as the inverse tangent function, is the inverse of the tangent function. It is denoted as arctan(x), atan(x), or tan^(-1)(x).
The arctan function takes a real number as input and returns the angle whose tangent is equal to that number. In other words, if y = arctan(x), then tan(y) = x.
In other words, the principal value of arctan refers to the primary angle within a specific range for which the tangent function yields a given value. In the case of arctan(2.6), we are seeking the principal angle whose tangent is equal to 2.6.
We can determine the principal value of arctan(2.6) to be approximately 1.231 radians or approximately [tex]70.43^o[/tex]. It is important to note that the angle can be expressed in either radians or degrees, depending on the desired unit of measurement.
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Find the product and express it in scientific notation. 3.1 × 10^-4 × 8.5 × 10^-2
Answer:
2.635 × 10⁻⁵
Step-by-step explanation:
(3.1 × 10⁻⁴) × (8.5 × 10⁻²)
2.635 × 10⁻⁵
-TheUnknownScientist
Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5 cards with the following amounts: $10, $20, $ 25, $30, $40. If Melissa receives one more card in the mail with $25, which of the following will happen?
Answer:
its will just add 25 to the total amount of money she got in the cards.
Step-by-step explanation:
Which geometric series diverges?
Answer:
1) not diverges
2)not diverges
3) diverges
4)not diverges
Step-by-step explanation:
In geometric series, If the |r|<1 then the series is convergent and if |r|>1 then the series is divergent
Where r is the ratio between the consecutive terms of series.
1) 3/5 + 3/10 +3/20 + 3/40 ......
in the above geometric series
r= (3/10) / (3/5)
= 1/2
= 0.5
As |r|= 0.5 < 1, so the series will not diverge
2) -10+4-8/5 + 16/25 -......
in the above geometric series
r= (4) / (-10)
= -2/5
= -0.4
As |r|= 0.4 < 1, so the series will not diverge
3) ∑ 2/3(-4)^(n-1)
in the above geometric series
r= -4
As |r|= |-4| = 4 > 1, so the series will diverge
4) ∑ (-12)(1/5)^(n-1)
in the above geometric series
r=1/5
= 0.2
As |r|= 0.2 < 1, so the series will not diverge !
Answer:
Its C!!!!!!!!!!
Step-by-step explanation:
Please help out with this QUestion thank chu very much
Answer:
The graph in the attached figure
The point (-1,4) represent a solution
Step-by-step explanation:
we have
[tex]x> -2[/tex]----> inequality A
[tex]y\leq 2x+7[/tex] ----> inequality B
using a graphing tool
The solution is the shaded area
see the attached figure
Remember that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution of the system of inequalities
The point (-1,4) represent a solution
Answer:
(-1,4)
Step-by-step explanation:
The given system of inequalities is:
x>-2:(red region)
[tex]y\le2x+7[/tex]: (blue region)
The graph of the system f inequalities is shown in the attachment.
The points that lies in the intersection of the red and blue region is the solution to the inequality.
From the graph (-1,4) is a solution to the system of inequalities.
write the standard equation of a circle with center (-2,5) and the point (4,13) on the circle
since the point (4,13) is on the circle, then the distance from the center to it, is the radius of the circle.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-2)]^2+[13-5]^2}\implies r=\sqrt{(4+2)^2+(13-5)^2} \\\\\\ r=\sqrt{36+64}\implies r=\sqrt{100}\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{5}{ k})\qquad \qquad radius=\stackrel{10}{ r}\\[2em] [x-(-2)]^2+[y-5]^2=10^2\implies (x+2)^2+(y-5)^2=100[/tex]