one number is 3 over 8 of another number. the difference of the two numbers is 4.2. what is the lesser number.
Answers
EXPLANATION
Let's analyze the problem:
3
Related Questions
Find the new price after the discount is applied. Round to the nearest cent if necessary.
$13.50 discounted 75%
Answers
Answer:
$3.38
Step-by-step explanation:
75% of 13.50=
0.75×13.50=
13.50-10.125=
3.375 = $3.38..(If we rounded to the nearest cent will be 3.38)
The graph shows the relationship between the distance traveled by car and the amount of fuel used by the car. What is the constant of proportionality for this graph?
1
1/20
2
20
Answers
Answer:
20
Step-by-step explanation:
Find the foci of the hyperbola that can be described by the equation
Answers
Solution
The two foci are (+ae, 0), and (-ae, 0)
\(\begin{gathered} e=\sqrt{1+\frac{b^2}{a^2}} \\ \\ a=6,b=8 \\ \\ \Rightarrow e=\sqrt{1+\frac{64}{36}}=\frac{5}{3} \end{gathered}\)\(ae=6\times\frac{5}{3}=10\)The answer is
Find the midpoint of the segment below and enter its coordinates as an
ordered pair. If necessary, express coordinates as fractions, using the slash
mark (/) for the fraction bar.
(-2,3) (10,3)
Answers
Answer:
(4,3)
Step-by-step explanation:
Midpoint formula
The midpoint of the line segment is given by M ( 4 , 3 )
What is the midpoint of two points?The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Measure the distance between the two end points, and divide by 2.
Let A ( x₁ , y₁ ) be the first point
Let B ( x₂ , y₂ ) be the second point
The midpoint between A and B is M ( a , b ) where
a = ( x₁ + x₂ )/2
b = ( y₁ + y₂ ) / 2
Given data ,
Let the first point be A ( -2 , 3 )
Let the second point be B ( 10 , 3 )
Now , let the midpoint of A and B be M ( a , b ) where
a = ( x₁ + x₂ )/2
b = ( y₁ + y₂ ) / 2
On simplifying , we get
a = ( 10 - 2 ) / 2
b = ( 3 + 3 ) / 2
On further simplification , we get
a = 4
b = 3
Hence , the midpoint is M ( 4 , 3 )
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A fifth grader takes a standardized achievement test (mean = 120, standard deviation = 8) and scores a 128. What is the child's percentile rank?
Answers
The child's percentile rank is 84.13%.
How do you determine the percentile?To determine the percentile rank of a score, you need to know the mean and standard deviation of the test, as well as the score in question. In this case, the mean is 120 and the standard deviation is 8.
To convert the child's score of 128 to a percentile rank, you would first convert it to a z-score using the formula (score - mean) / standard deviation = z-score.
In this case:
(128 - 120) / 8 = 1
This z-score of 1 represents the number of standard deviations above the mean the child's score is. To convert this z-score to a percentile rank, you can use a table of the standard normal distribution, which shows the proportion of values that are less than or equal to a given z-score.
A z-score of 1 corresponds to a percentile rank of 84.13%
So, the fifth grader who scored 128 on a standardized achievement test has a percentile rank of 84.13%. This means that 84.13% of students scored lower than the child on this test.
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Question provided in attachment.
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We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.
How to calculate the valueSample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18
= 480 / 18
≈ 26.667
Sample Standard Deviation (s):
= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))
≈ ✓(319.778 / 17)
≈ ✓(18.81)
≈ 4.336
Confidence level = 99%
Sample Size (n) = 18
Sample Mean = 26.667
Sample Standard Deviation (s) = 4.336
Degrees of Freedom (df) = n - 1 = 18 - 1 = 17
Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.
Margin of Error (E) = 2.898 * (4.336 / ✓18))
≈ 3.748
Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)
= (22.919, 30.415)
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.
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Last week, the Tasha Cola company had sales of $2,346.87. This week, the company had sales of $8,867.14. Which is the best estimate of the company’s total sales for both weeks?
Answers
Answer:
$11,200 or $11,000
Step-by-step explanation:
The amounts are approximately $2,300 and $8,900 which add up to $11,200.
Answer: $11,200 or $11,000
It seems there are choices for this problem, but you did not include them, so I can't tell the exact correct answer.
A six sided fair die is rolled with two coins, all sides of a fair die have equal chances of being displayed ,Find the probability of no heads.
Answers
PLEASE HELP!!! Solve 5sin(π/3x)=3 for the four smallest positive solutions
Answers
This one's a special case of a right angled triangle with sides (3, 4, and 5 units)
Back to the problem :\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)
Now, check the triangle, sin 37° = 3/5
therefore,
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)
[ convert degrees on right side to radians ]
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)
There are three more possible values as :
\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)
\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)
\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)
Equating both, we get : First value :\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)
\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)
or in decimals :
\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)
[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]
similarly,
Second value :\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)
Third value :\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)
Fourth value :\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)
" x can have infinite number of values here with the same result, here are the four values as you requested "
I hope it was helpful ~
For what purpose do you think the following persons would need to collect data for Hotel Manager and Hospital adminstrator?
Answers
Given: Two different persons (a) Hotel manager (b) Hospital Administrator
To Determine: What purpose we think each person would need to collect data
I think the purpose a hotel manager would need to collect data are
(i) understand guest's habit
(ii) predict decison
(iii) understand guest's preferences
I think the purpose a hospital adminstrator would need to collect data are
(i) Improve the quality of services provide to patients
(ii) Predict decision
(iii) to prevent outbreak before they happen
Della wants to make a one-sample interval to estimate what proportion of her community members favor a
tax increase for more local school funding. She wants her margin of error to be no more than -2% at the 95%
confidence level
What is the smallest sample size required to obtain the desired margin of error?
Answers
Answer:
2401
Step-by-step explanation:
khan
The data on the right represent the number of traffic fatalities by seat location and gender. Determine P() and P(|). Are the events "" and "" independent? Total Total Determine P(). P() . 318 (Round to three decimal places as needed.) Determine P(|). P(|) . 264 (Round to three decimal places as needed.) Are the events "" and "" independent? A. Yes. The occurrence of the event "" affects the probability of the event "." B. No. The occurrence of the event "" affects the probability of the event "." C. No. The occurrence of the event "" does not affect the probability of the event "." D. Yes. The occurrence of the event "" does not affect the probability of the event "."
Answers
Answer:
The probability of selecting a male is 0.3151.
The events "male" and "driver" are not independent.
The correct option is B.
Step-by-step explanation:
The missing data is as follows:
Female Male Total
Driver 32759 11715 44474
Passenger 6534 6361 12895
Total 39293 18076 57369
The complete question is:
Determine P(male) and P(male|driver). Are the events "male" and "driver" independent?
Solution:
Compute the probability of selecting a male as follow:
\(P(M)=\frac{n(M)}{N}=\frac{18076 }{57369}=0.3151\)
Thus, the probability of selecting a male is 0.3151.
Compute the probability of selecting a male given that he is a driver as follows:
\(P(M|D)=\frac{P(M\cap D)}{P(D)}=\frac{n(M\cap D)}{n(D)}=\frac{11715 }{44474}=0.2634\)
Two events, say A and B, are independent if:
P (A|B) = P(A)
Here, P (M|D) ≠ P (M)
Thus, the events "male" and "driver" are not independent.
P(female)= .317
Determine P(femaleIpassenger)= .264
No. The occurrence of the event
"passenger" affects the probability of the event "female."
PLS HELP The histogram displays donations in dollars to a charity. A histogram titled Donations to Charity In Dollars with the x-axis labeled Donations. The x-axis has intervals of 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Number of Donations and starts at 0 with tick marks every one unit up to 5. There is a shaded bar above 10 to 19 that stops at 4, above 20 to 29 that stops at 3, above 30 to 39 that stops at 1, and above 50 to 59 that stops at 1. There is no shaded bar for 40 to 49. Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 49. This might happen if the charity suggested donation minimum of $35 and donors followed that.
The data is skewed, with a maximum range of 49. This might happen if the donations were only allowed in cash and many donors did not have much cash on them.
The data is bimodal, with a maximum range of 49. This might mean that the most popular amounts to donate were between 10 and 19 and 51 and 59 dollars.
The data is symmetric, with a maximum range of 59. This might happen if everyone donated a percent of their salaries.
Answers
Based on the given histogram, the data is skewed with a maximum range of 49.
This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.
One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.
Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.
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Marco can hit the archery target 3 out of every 15 times he shoots. If he missed 48 times, how many times will he be expected to hit the target?
Answers
Answer: 12
15-3=12 miss ratio
48misses/12 sets of misses= 4 sets of 15 shots
Up to twelve 4*3 twelves accurate shots provided he shot at least 60
Step-by-step explanation:
what is 20 squared 2 + 6(9 + 3)
Answers
Answer:
\(\sf 872\)
Step-by-step explanation:
Parentheses
\(9 + 3 = 12\)
\(=20^2\cdot \:2+6\cdot \:12\)
Exponents
\(20^2=400\)
\(=400\cdot \:2+6\cdot \:12\)
M/D(Multiply/Div.)
\(6\cdot \:12 = 72\)
\(=800+72\)
A/S(Add/Sub.)
\(800+72=872\)
\(\sf Thus,\\= 872\)
In the figure below, m ZWXZ=68°, and m L 1 is three times m L 2. Find m L 2.
Answers
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Explain about the Angle?The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees.
Angle ZWXZ was divided into two angles, 1 and 2, by XY.
Given that 1 is three times 2, angle 1 would be represented by 3x if we let x represent 2.
m<1 + m<2 equals m<ZWXZ
68 add like terms for 3x + x
Divide both sides by 4 if 4x = 68
x=17
The measure of angle 2 is 17 since x = 17
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The measure of angle 2 is 17 since x is 17.
Explain about the Angle?The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees.
Angle ZWXZ was divided into two angles, 1 and 2, by XY.
Given that 1 is three times 2, angle 1 would be represented by 3x if we let x represent 2.
m<1 + m<2 equals m<ZWXZ
68 add like terms for 3x + x
Divide both sides by 4 if 4x = 68
x=17
The measure of angle 2 is 17 since x = 17
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Distance from earth to the moon is 238,900 . From earth to the sun is 92935,700 ,about how many times the distance from earth to the moon is distance from earth to the sun
Answers
Answer: the sun is 389.015069067 times further away from earth to the moon
Step-by-step explanation: 92935700/238990=389.015069067
Suppose that the number of customers that enter a bank in a hour is a poisson random varialbe, and suppose that P(x=0)=0.07, Determine the mean and variance of x
Answers
The mean and the variance of the poisson distribution are;
Mean = 2.66
Variance = 1.277
How to solve Poisson Distribution problems?The formula for the PMF of a Poisson distribution is;
p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......
Thus;
p(x = 0) = [e^(-λ) * λ^(0)]/0!
e^(-λ) = 0.07
λ = - In 0.07
λ = 2.66
That is the mean
Variance is square root of standard deviation;
Variance = √√(2.66)
Variance = 1.277
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Answer:
2.65926003693 for mean and variance.
Step-by-step explanation:
First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.
If 4x – 3 = 2x + 9, then x = ?
Answers
Answer:
x=6
Step-by-step explanation:
subtract the 2x from 4x and add 3 to 9. we would get 2x=12. divide by 2 on both sides and you get x=6!
Después de leer un libro sobre el antiguo
Egipto, Cassie decidió construir con cartón un
modelo de una pirámide.
30 cm
25 cm
Answers
Cassie need to make the model is 2250 cm²
What is square pyramid?A square pyramid has a square base and four lateral faces in geometry. A pyramid is a polyhedron with a base and three or more triangular faces that meet above it .
The complete question is attached below:
We know,
A= a(a+ √(a²+4h²))
and, a =25cm, h=30 cm
So,
A= 25(25+ √(25²+4*30²))
=25(25+65)
= 2250 cm²
Hence, Cassie need to make the model is 2250 cm²
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Find the required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly for an annuity.
Round to 2 decimals places.
Answers
The required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly for an annuity is approximately
$264.62How to find the paymentTo find the required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly, we can use the formula for the future value of an ordinary annuity:
FV = P * (1 - (1 + r)⁺ⁿ) / r,
where:
FV is the future value of the annuity ($28,000),
P is the monthly payment we want to find,
r is the monthly interest rate (5.4% / 12 = 0.0045),
n is the total number of payments (12 years * 12 months = 144).
Plugging in the values, we have:
28000 = P * (1 - (1 + 0.0045)⁺¹⁴⁴) / 0.0045.
28000 = P * (1 - 0.5239) / 0.0045.
28000 = P * (0.4761) / 0.0045.
28000 = P * 105.8107.
p = 264.6235
P ≈ $264.62 (rounded to 2 decimal places)
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Which of the following equations shows how substitution can be used to solve the following system of equations? \((y = 2x - 7 \\ 3 \times + 4y = 16\)A: 3(2x-7) + 4y = 16B: 3x + 4(2x-7) = 16 C: y = -7D: 3x + 4y = 2x - 7
Answers
Answer:
B: 3x + 4(2x-7) = 16
Explanation:
The system of equations is
y = 2x - 7
3x + 4y = 16
To solve the system of equations by substitution, we need to substitute the first equation on the second equation. Since y = 2x - 7, we will replace y by 2x - 7 on the second equation, so
3x + 4y = 16
3x + 4(2x - 7) = 16
Therefore, the answer is:
B: 3x + 4(2x-7) = 16
Guys anyone please help . Please explain how to solve these questions it gives the answers but I need expiation (Calculus) ,I’ll give brainliest for the correct answer ! Pleasseee
Answers
9514 1404 393
Answer:
(ii) center: (-3, 6)
(iii) A(-3, 6-√51), B(7, 6), D(-3, 6+√51), H(-13, 6)
(iv) (x +3)²/100 +(y -6)²/51 = 1
Step-by-step explanation:
(ii) The center is the midpoint between the foci:
center = ((-10, 6) +(4, 6))/2 = (-10+4, 6+6)/2
center = (-3, 6)
__
(iii) The vertices are the center plus or minus the semi-major axis length in the x-direction: (-3±10, 6).
The semi-minor axis length is the root of the difference of squares of the semi-major axis and the center-focus distance:
semi-minor axis = √(10² -7²)
semi-minor axis = √51
So, the co-vertices are the center plus or minus this value in the y-direction: (-3, 6±√51)
Using the labeling in the drawing the various points are ...
A(-3, 6-√51), B(7, 6), D(-3, 6+√51), H(-13, 6)
__
(iv) For center (h, k) and semi-axis lengths 'a' and 'b' the equation of an ellipse is ...
(x -h)²/a² +(y -k)²/b² = 1
For the center and axes here, the equation is ...
(x +3)²/100 +(y -6)²/51 = 1
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
Fred brought a shirt and a wallet for a total of 34.26 before tax. The price of the wallet was $15 less than the price of the shirt. What was the price of the shirt?
Answers
Answer:
The price of the shirt is $24.63.
Step-by-step explanation:
Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:
x + (x - 15) = 34.26
Simplifying, we get:
2x - 15 = 34.26
Adding 15 on both sides:
2x = 49.26
Dividing by 2:
x = 24.63
Therefore, the price of the shirt is $24.63.
at a baseball game a vender sold a combined total of 141 sodas and hot dogs. the number of sodas was 51 more than the number of hotdogs sold. Find the number of sodas sold and the number of hot dogs sold
Answers
Hot Dogs: 45
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
Number 5 Please look at image
Answers
The solutions to the quadratic equations are as follows
4a. The rocket was launched from an initial height of 10 meters.
b. The maximum height of the rocket was 55 meters.
c. The rocket reaches its maximum height at 3 seconds
d. the rocket is in the air for t = 6.316 seconds
5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet
b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.
How do we solve the quadratic equation?The function is a quadratic equation, and here is how we solve each problem;
a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:
h = -5(0)² + 30(0) + 10 = 10 meters
b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:
t = -b/2a = -30 / (2×-5) = 3 seconds
So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:
h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters
The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:
0 = -5t² + 30t + 10
This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)
Let's calculate the roots:
t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)
= [-30 ± √(900 + 200)] / -10
= [-30 ± √(1100)] / -10
= 6.316 or -0.32
5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:
h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet
b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:
h = -1/8(33)² + 4(33) + 5
h = -1/8×1089 + 132 + 5
h = -136.125 + 132 + 5
h = 0.875 feet
when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.
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im lost can someone help?
Answers
Someone help me please and thank you
Answers
Answer: 2a < 2b
Step-by-step explanation:
We are given a statement:
a < b and b < c, then 2a ____ 2b
We can use simple numbers that make the statement true.
Where,
a = 2
b = 3
c = 4
Now lets plug it in.
2 < 3 and 3 < 4, then 2(2) ____ 2(3)
and lets simplify:
2 < 3 and 3 < 4, then 4 ____ 6
We can see that 4 is less than 6,
so as a is less than b, 2a is less than 2b.
The only thing changing is the coefficient being multiplied by the variables a and b.