In this problem the function that models the hight is:
[tex]h(t)=-5t^2+14t+3[/tex]So when the water hits the grownd h=0 so we replace that and solve for t so:
[tex]0=-5t^2+4t+3[/tex]To solve this expression we can use the cuadratic equation:
[tex]x=\frac{-4\pm\sqrt[]{16-4(-5)(3)}}{-10}[/tex]and we operate so:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{76}}{-10} \\ x=\frac{-4\pm8.7}{-10} \end{gathered}[/tex]Now we solve bout of the equation so:
[tex]\begin{gathered} x_1=\frac{-4+8.7}{-10}=-0.47 \\ x_2=\frac{-4-8.7}{-10}=1.27_{} \end{gathered}[/tex]So the answer that have sense is the secon one so the water hits the ground after 1.27 seconds
What is the total amount of the monthly payments for a $6,100, two-year loan with an APR of 5%? Round to the nearest dollar.
Based on the amount of the loan, and the number of periods as well as the APR, the total amount of the monthly payment would be $6,423.
How to find the total monthly payments?The monthly payments for the loan would be constant so they can be considered to be annuities.
The value of these annuities would be:
Present value of annuity = Annuity x ( 1 - (1 + rate)^-number of periods) / rate
6,100 = Annuity x (1 - (1 + 5%/12)⁻⁽²ˣ¹²⁾ / 0.05/12)
Annuity = 6,100 / 22.793898393955992921598741250451
= $267.62
The total monthly payment is:
= 267.62 x 12 x 2 years
= $6,423
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in the graph, the coordinate point (4,-9) is ____in the graph, the coordinate point (1,0) is ____in the graph, the coordinate point (7,0) is ____in the graph, the coordinate point (4,0) is ____the options: an x-intercept, a y-intercept, a vertex, on the line of symmetry
Answer:
In the graph, the coordinate point (4,-9) is a vertex
In the graph, the coordinate point (1,0) is an x-intercept
In the graph, the coordinate point (7,0) is an x-intercept
In the graph, the coordinate point (4,0) is on the line of symmetry.
Explanation:
The x-intercepts are the points where the parabola crosses the x-axis, so the coordinates of the x-intercepts are (1, 0) and (7, 0)
The y-intercept is the point where the parabola crosses the y-axis, so the y-intercept is (0, 7)
The vertex is the minimum point of the parabola, in this case, (4, -9).
The line of symmetry depends on the first coordinate of the vertex, so the line of symmetry is x = 4. It means that any point with a first coordinate equal to 4 is on the line of symmetry.
Then, the answers are:
In the graph, the coordinate point (4,-9) is a vertex
In the graph, the coordinate point (1,0) is an x-intercept
In the graph, the coordinate point (7,0) is an x-intercept
in the graph, the coordinate point (4,0) is on the line of symmetry.
4. multiple choice: as the sample size n increases, the distribution of sample means: a. becomes narrower b. remains constant c. becomes wider 5. multiple choice: according to the central limit theorem, the mean of the sample means is: a. less than the population mean b. the same as the population mean c. more than the population mean 6. multiple choice: according to the central limit theorem, the standard deviation of the sample means is: a. less than the population standard deviation b. the same as the population standard deviation c. more than the population standard deviation
The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.
What is meant by the population mean?The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.
The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).
Therefore, the correct answer is option a. less than the population mean.
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The shortest side of a right triangle measures 6, and the longest side measures 10. Determine the measurement of the unknown side.
5
8
9
10
In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.
How can the measurement of the unknown side be calculated?We can use this expression from trigonometry to know the third side of the triangle as:
a^2 + b^2 = c^2
Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :
10^2 - 6^2
The we can simplify as
100-36=64
Then [tex]\sqrt{64}[/tex] = 8.
Therefore, the second option is correct.
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5 + 7(6 −4) − 2(5 − 1)
Answer: 11
Step-by-step explanation:
5 + 7(6-4) - 2(5 - 1)
P E M/D A/S
5 + 7(2) - 2(4)
P E M/D A/S
5 + 14 - 8
P E M/D A/S
11
Algebraically solve for x: 7/2x-2/x+1=1/4
Step-by-step explanation: Check the photo
Answer:
x = -2
Step-by-step explanation:
7/(2x) - 2/x + 1 = 1/4
7/(2x) - 4/(2x) + 1 = 1/4
(7-4)/(2x) = 1/4 - 1
3/(2x) = 1/4 - 4/4
3/(2x) = - 3/4
3 = (-3/4)(2x)
3 = -6x/4
3*4 = -6x
12 = -6x
12/-6 = x
-2 = x
Check:
7/(2*-2) - 2/-2 + 1 = 1/4
7/-4 + 1 + 1 = 1/4
-7/4 + 2 = 1/4
-7/4 + 8/4 = 1/4
The diagram show that PQR and SQT are straight lines.
Find the value of
As per the angle sum property, the value of x is 125°
Angle sum property:
According to the angle sum property, the sum of interior angles of a triangle is 180°.
Given,
In the given diagram, PQR and SQT are straight line.
Now we need to find the value of x.
As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.
While we equate the given values within this property, we get.
x° + 55° = 180°
x° = 180° - 55°
x° = 125°
Therefore, the value of x is 125°.
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Choose a relationship model that will reach $0 in the same number of days as this scenario: mika has $12 and spends $2 each day. y = â€""2x â€"" 12 y = â€""3x 18 y = â€""4x 12 y = â€""12x 2
The equation that represent the relationship model that will reach $0 in the same number of days as the scenario gave is: y = -2x + 12
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Mika has = $12Mika spend = $2 per dayDay = xy = $0Writing the equation according to the information gave, we have:
y = -2x + 12
Where:
y = 0$x = daysSo that (y) equals zero, the number of days (x) should be = 6
y = -2x + 12
0 = -2*6 + 12
0 = -12 + 12
0 = 0
The "y" variable is the dependent variable, because it will change according to the number of days passed (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of days passed.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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What is the result when 2a - 5 is subtracted from 3a + 3?
Answer:-1a+2
Step-by-step explanation:
add like terms
Hey there!
(2a - 5) - (3a + 5)
= 2a - 5 - 3a + 5
COMBINE the LIKE TERMS
= (2a - 3a) + (-5 + 3)
= 2a - 3a + (-5) + 3
= -1a - 2
Therefore, your answer should be:
-1a - 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
My friend sandy bought 3 pair of jeans and 7 shirts for $60. my friend dan bought 2 pair of jeans and 3 shirts for $30. what are the prices for jeans and shirts?
The prices for jeans and shirts are $6 and $6
Calculations and ParametersGiven that:
3 pairs of jeans and 7 shirts for $60.
And 2 pairs of jeans and 3 shirts for $30.
Let jeans be x
Let shirts be y
3x + 7y = 60.... eq 1
2x + 3y = 30...... eq 2
Let us make x the subject formula from equation 2
2x = 30-3y
x= (30-3y)/2..... eq 3
Put the value of x into equation 1
3 * (30-3y)/2 + 7y = 60
(90- 9y)/2 + 7y = 60
45 - 4.5y + 7y = 60
2.5y =15
y = 6
Then, put the value of y into eq 3
x= (30-3(6))/2
x= 15 - 9
x= 6
Hence, we can see that the values of x and y are 6 apiece.
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Answer:
yeah it's correct , very much well
Please help, i really need help
Answer:
Angle 1: 159
Angle 2: 21
Angle 4: 21
Step-by-step explanation:
If sin A 0.3, cos A = 0.7, sin B = (1/√5)
and cos B: (-1/√5) find the exact value of cos(A - B).
(i know the answer but i want to know how to solve it as well)
The exact value of cos(A - B) is -2√5 /25.
What are Sine and Cosine?In math, the trigonometric functions of an angle are sine and cosine. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the lengths of the adjacent leg to the hypotenuse, and the sine of the specified angle is the ratio of the opposite leg's length to the hypotenuse's length.The concepts of sine and cosine can be expanded to include any real value in terms of the lengths of particular line segments in a unit circle.The sine and cosine can be extended to any positive or negative value, even complex numbers, according to more recent definitions of the terms, which also represent them as infinite series or as the solutions to specific differential equations.Therefore,
sin A = 0.3
sin B = (1/√5)
cos A = 0.7
cos B = (-1/√5)
cos(A-B) = cos a cos b + sin a sin b
⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))
⇒ cos(A-B) = -0.7/√5 + 0.3/√5
⇒ cos(A-B) = -0.4/√5
On multiplying, √5 on the numerator and denominator,
⇒ cos(A-B) = -0.4 x √5 / 5
⇒ cos(A-B) = -2√5 /25
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Robert gets a loan from the bank. agrees to borrow 6000 , his interest rate is 7 %. he agrees to pay back over a 10 year period. how much money wil he have paid back by then?
The amount to be paid after paying interest of 7% for 10 years is 10,2000
The amount to be borrowed from the bank = 6000
Interest rate for the amount per year = 7%
The total time period of the loan = 10 years
Thus , the final amount can be calculated by using the formula
A = P(1 + rt)
where A is the final amount
P is the principal amount to be borrowed
r is the rate of interest
t is the time period
Now, let us substitute the known values in the above equation , we get
A = 6000 ( 1 + 0.07 x 10)
= 6000 (1 + 0.7)
= 6000 (1.7)
A = 10,200
Therefore , the final amount to be paid is 10,200
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f(x)=6x^2+11 inverse
Answer:
√6(x−11)/6
Step-by-step explanation:
f^−1(x)=√6(x−11)/6
after sampling a column of water from the surface to a depth of 3000 meters (nearly 10,000 feet), a colleague aboard an oceanographic research vessel tells you that the water column is isopycnal. what does this mean? what conditions create such a situation? what would have to happen in order to create a pycnocline?
6V
6V
I
I₁
R₁ =
6Ω
IT
B₁
1₂
R₂
352
B₂
Series or parallel?
m
VT=
V Branches
1₁ =
1₂=
IT =
RT =
P =
Answer:
12
Step-by-step explanation:
1) Round the number to the underlined place value.
-17.625
$ Given T is the midpoint of SU. Prove x = 5 3x + 20 STATEMENTS REASONS 1. 1. Given 2. ST = TU 2. Definition of midpoint W 3. Definition of congruent segments 3. ST = TU 4. 7* = 3x + 20 4. 5. 5. Subtraction Property of Equality 6. r = 5 6. 1. What should be the statement for Reason 1? SU = SU
In the images, we are given an exercise which is solved by taking T as the midpoint of SU. This is the
a) Write an equation of a line in point slope form given the slope -2/3 and the point (-3,2). b) Write an equation in slope intercept form through the points (3,-3) and (2,0) c) write an equation based on this model. Gas cost $4.00 per gallon. If someone paid a startup fee of 5.00, write an equation in slope intercept form based on this model in y = mx+b
Answer:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]Explanation:
Here, we want to write the equation of a line in point-slope form
Mathematically, we have that as:
[tex]y-y_1=m(x-x_1)[/tex]where m, which is the slope is -2/3 and (x1,y1) which is the point is (-3,2)
Substituting the values, we have it that:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]Order the fractions from smallest to largest. 3/4, 4/6, 1/2, 5/8
To solve the exercise you can rewrite the fractions in decimal form and then we order.
To write them in decimal form divide the numerator by the denominator, then we have
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{4}{6}=0.67 \\ \frac{1}{2}= \end{gathered}[/tex]HELP ME PLEASE ANY HELP WILL BE APPRECIATED
Answer:
a) Yes, the graph is proportional. It is linear and it goes through the point (0,0)
b) No shells cost no dollars
c) 3 shells cost 1.20
Step-by-step explanation:
To graph this, you only need 2 points. You have the points (0,0). You can put a point at (0,0) and at the point ( (3, 1.20) and then draw a line through those 2 points.
Which of the following values are solutions to the
inequality 9 ≤ 3x +4?
I. - 7
II. 8
III. 2
Answer:
II. 8
III. 2
Step-by-step explanation:
Solving an inequality
9 ≤ 3x +4
Subtract 4 from each side
9-4 ≤ 3x +4-4
5 ≤ 3x
Divide each side by 3
5/3 ≤ 3x/3
5/3 ≤ x
x must be greater than or equal to 5/3
I. - 7 this is not greater than or equal to 5/3
II. 8 this is greater than or equal to 5/3
III. 2 this is greater than or equal to 5/3
the gmat scores of all examinees who took that test this year produced a distribution that is approximately normal with a mean of 410 and a standard deviation of 33. the probability that the score of a randomly selected examinee is less than 370, rounded to three decimal places, is:
The probability that the score of a randomly selected examinee is less than 370 is 0.113
Mean of the gmat score = 410
Standard deviation of the deviation = 33
The randomly selected examinee be X ,
Thus X = 370
So , we need to find the probability that the score of a randomly selected examinee is less than 370 i.e.
P(X < 370)
Now , let us the z-score with normal distribution formula
Z = (X - μ) / σ
Z = (370 - 410) / 33
Z = -40 / 33
Z = -1.21
Thus P(X < 370) = P(Z < -1.21)
From the z - table , we can get that
P(Z < -1.21) = 0.11314
By rounding off to three decimals ,
P(Z < -1.21) = 0.113
Therefore , the probability of Z< -1.21 is 0.113
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What angle does a 3.8 m ladder make with the ground if it reaches 2.1 m up the wall? How far is the foot of the ladder from the wall?
The angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters
The length of the ladder = 3.8 meter
The length of wall = 2.1 meter
Draw the figure using the measurements
We have to use the trigonometric function
The angle that a ladder make with the ground
sin θ = Opposite side / Hypotenuse
sin θ = 2.1/3.8
θ = 33.54 degrees
The distance from the foot of the ladder from the wall
cos θ = Adjacent side / Hypotenuse
cos 33.54 = Adjacent side / 3.8
Adjacent side = 3.8 × cos 33.54
= 3.16 meters
Hence, the angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters
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EB.AACB = ADCE. AB = 8 and AC = 6DE = [?]
DE will be equal to AB, then DE=8
A 12-ft-by-15-ft rectangular swimming pool has a 3-ft-wide no-slip surface around it. What is the outer perimeter of the no-slip surface?.
The outer perimeter of the no-slip surface is 78 feet if the swimming pool has a 3-ft-wide no-slip surface around it.
The outer perimeter of an area or land can be described as the whole of its outer edge or can be described as the sum total of the outside edge lengths.
We can find the outer perimeter of this swimming pool by adding 3 feet twice to all the sides of this rectangular swimming pool followed by the addition of these sides together.
As the swimming pool is 12-ft-by-15-ft, this represents that two sides of this rectangular swimming pool are 15 feet and the other two sides are 12 feet, therefore;
12 + 6 = 18
15 + 6 = 21
Now we can find the perimeter by the addition of all the sides as follows;
18 + 18 + 21 + 21 = 78 feet
Therefore, the outer perimeter of the no-slip surface is found to be equal to 78 feet.
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Angel earned $70 mowing lawns, which is 140% of the amount George earned. How much money did George earn?
The total amount earned from mowing lawns by George is $50
How to determine the amount earned by George?From the question, we have the following parameters that can be used in our computation:
Earnings percentage = 140%
Angel total earnings in mowing lawns = $70
The amount earned from mowing lawns by George is then calculated as
Angel total earnings in mowing lawns = Earnings percentage x Total amount earned from mowing lawns by George
Substitute the known values in the above equation
So, we have
70 = 140% x Total amount earned from mowing lawns by George
Divide both sides by 140%
Total amount earned from mowing lawns by George = 50
Hence, the total amount is $50
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The Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 20 jars, and in 5 hours, it bottles 50 jars of honey.
Determine the constant of proportionality.
(HELP THIS IS OVERDUE !!)
Answer:
9
Step-by-step explanation:
because in one hour it fills 18÷2 =9.
Answer: It's 10 because 20* Divided by 2 is 10
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!
Which box-and-whisker plot matches the data?
5, 8, 4, 2, 5, 9, 7, 12, 4, 3
A.
A box and whisker plot is shown above a number line that extends from 0 to 20 with 1 unit markings. The box extends from 4 to 8, with the median at 6. There is also a point marked at six. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.
B.
A box and whisker plot is shown above a number line that extends from 0 to 20 with 2-unit markings. The box extends from 4 to 8, with the median at 7. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.
C.
A box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 2 to 12, with the median at 5. There are points marked at 2, 5, and 12.
D.
A box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 4 to 8, with the median at 5. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.
The box plot that matches the data is a box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 4 to 8, with the median at 5. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.
What is a box and whisker plot?A box and whisker plot is a graph that is made up of two lines and a box. The two lines are known as whiskers. The end of the first whisker is the minimum value and the end of the second whisker is the maximum value.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
The data : 2, 3, 4, 4, 5, 5, 7, 8, 9, 12
Minimum = 2 Maximum = 12 First quartile = 1/4 x (10 + 1) = 5.5 term = 3.5Median = 5Third quartile = 3/4 x (10 + 1) = 8.25 term = 8To learn more about box and whisker plots, please check: https://brainly.com/question/27215146
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Write the numbers from greatest to least -2.1, -1 5/6, -1 2/3, -2.2
In form of a/b
The numbers from greatest to least is - 1 2/3, -1 5/6, -2.1 and -2.2.
How to calculate the values?Based on the information, we want to arrange the numbers from the greatest to the least.
In this case, it will be illustrated thus:
-2.1
-1 5/6 = -1.83
-1 2/3 = -1.67
-2.2
This will be arranged as - 1 2/3, -1 5/6, -2.1 and -2.2. In this case, it can be deduced that - 1 2/3 is the greatest and the least number is -2.2. This shows the concept of descending numbers.
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