If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .
In the question ,
it is given that
the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula
v = √(19.6×h)
to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,
we substitute v = 25.7 in the equation v = √(19.6×h) ,
we get ,
25.7 = √(19.6×h)
squaring both the sides , we get
19.6 × h = 25.7²
19.6 × h = 660.49
h = 660.49/19.6
h = 33.698
h ≈ 33.7
Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .
The given question is incomplete , the complete question is
Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?
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Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not.
1) Is this an experiment? If not, what kind of study is it?
2) Is it correct to conclude that shorter men are at higher risk of dying from a heart attack? Explain.
A. Yes, since the result is considered to be statistically significant.
B. No, since there may be confounding variables interfering with the treatment, such as patient age or weight.
C. No, since it cannot be determined which of the subjects will die from heart attacks in the future.
D. No, since there may be lurking variables, such as patient age or weight.
1. It is an experiment and the kind of study is the case - control study.
2. We can't conclude that shorter men are at higher risk of dying from a heart attack ad D. No, since there may be lurking variables, such as patient age or weight.
What is a case - control study?It should be noted that a case control study is an observational study where there are two groups that are compared based on certain attribute.
It should also be noted that it's an experiment as a research was made to get some needed information about heart attack.
Lastly, we can't conclude that shorter men are at higher risk of dying from a heart attack as some other variables are missing from the information provided.
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Rice costs ₤1.88 per kg in London. (₤ stands for British Pound) If the exchange rate for ₤'s and American $'s is ₤1.18 = $1, and 1 pound is equal to .454 kg, determine the price per pound of rice in London. State your answer rounded to the nearest cent. Be sure to include the units
Using metric units, the cost of rice in London is ₤0.85 per pound
Conversion of Metric UnitsTo solve this problem, we need to convert the price per kilogram to price per pound.
We can use the conversion factor of
1 pound = 0.454kg
And
$1 = ₤1.18
Let's proceed to convert from kilogram to pounds since the currency is already in the desired unit.
1lb = 0.454kg
x = 1kg
x = 1 / 0.454
x = 2.2lb
This implies that
₤1.88 = 2.2lb
x = 1lb
x = (1.88 * 1) / 2.2
x = 0.85
This becomes ₤0.85 per pound
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Is the function 4y = 24 linear or nonlinear?
The given function is linear and constant because your equation is represented by the standard form for the linear equation.
Which is a Linear Function?
A linear function can be represented by an equation. The standard form for the linear equation is: y= mx+b , for example, y=6x+4. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=6 and b=4.
An equation is classified as nonlinear when it is not represented by the standard form for the linear equation. For example, 2x²+x+10, x², x³, x³ +2, etc.
The given equation is 4y=24. Firstly, you should rewrite it to the standard form for the linear equation is: y= mx+b. Therefore,
4y=24
y=24/4
y=6
If the standard form for the linear equation is y= mx+b, for the given equation m=0 and b=6. Thus, the given equations is linear and constant. It can be classified for constant because for any value of x, the value of y always be equal to 6.
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Paid out amount is what percent of the recieved amount
Received amount - £567.89
Paid amount - £412.00
Answer: 72.5%
Step-by-step explanation: Since you want the percent of the paid amount of the received amount this will be your equation: paid/received. So if you do 412/567.89, you get ≈ .725 or 72.5%.
Explain the five properties of multiplication.
Find the matrix A of the linear transformation T from R2 to R2 that rotates any vector through an angle of 60∘ in the clockwise direction.
Any vector can be rotated via a 60 degree angle in the clockwise direction using the linear transformation from R2 to R2, and the corresponding matrix is
[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
What does a matrix for an angle alpha that is counter-clockwise mean?
An angle's matrix for counter clockwise rotation is
[tex]\left[\begin{array}{ccc}cos (alpha) &-sin (alpha) \\-sin (alpha)&cos (alpha)\end{array}\right][/tex]
Alpha angle matrix for a clockwise direction
Put alpha = -alpha in the matrix shown above.
The matrix above becomes
[tex]\left[\begin{array}{ccc}cos (alpha) &sin (alpha) \\sin (alpha)&cos (alpha)\end{array}\right][/tex]
if alpha = 60 degrees
The matrix above becomes
[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
Consequently, the matrix for the linear transformation from R2 to R2 that rotates any vector by 60∘ degrees in the clockwise direction.
is .[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
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A rectangular floor is 5 yd long and 4yd wide. Jessica wants to tile the floor with tile sold by the square foot. Use the facts to find the area in square feet.
The area in square feet is 180.
Given:
There is a rectangular floor is 5 yd long and 4 yd wide.
Required:
Jessica wants to tile the floor with tile sold by the square foot
Now, According to the question:
First of all we need to convert the given data in foot from yd.
We know that:
1 yd = 3feet
4 yd = 12 feet
5 yd = 15 feet
Now find the area of rectangular floor
Length of the floor = 5 yd = 15 feet
Breadth of the floor = 4 yd = 12 feet
Area = l x b
Area of the rectangular floor is :
15 x 12 = 180 feet sq.
Hence, The area in square feet is 180.
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Five more than a number is at most 17
Answer:
Im not sure but I think the answer is 6, but only if the total amount is for sure 17
Step-by-step explanation:
This is because we know that whatever the number is is five more than the unknown number and equals 17. This can be written as n + (5 + n) = 17, which can be simplified to x = 6.
Damon is saving for a vacation. He estimates that he’ll need about $2,500 for the trip. He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal. In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation. Review his work, and select the true statement. Step 1: y = 500 + 400x Step 2: y − 500 = 500 + 400x − 500 Step 3: y − 500 = 400x Step 4: y − 500 400 = 400 x 400 Step 5: y − 500 400 = x Step 6: 2 , 500 − 500 400 = x Step 7: 5 = x A. Damon used the multiplication property of equality in step 2. B. Damon used the subtraction property of equality in step 3. C. Damon used the division property of equality property in step 4. D. Damon used the associative property in step 5. E. Damon used the addition property of equality in step 6.
By reviewing Damon's work, the true statement is, Damon used the subtraction property of equality.
what is true statement?
A statement is true if the assertion it makes is true, and it is false if the assertion it makes is untrue. For example, the statement "The trains are always late" is only accurate if the situation it describes—that is, if the trains are indeed always late—actually exists.
As given, Damon is saving for a vacation.
He estimates that he’ll need about $2,500 for the trip.
He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal.
In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation.
The statements are,
Step 1: y = 500 + 400x
Step 2: y - 500 = 500 + 400x - 500
Step 3: y - 500 = 400x
Step 4: y - 500/400 = 400x/400
Step 5: y - 500/400 = x
Step 6: 2500 - 500/400 = x
Step 7: 5 = x
Therefore, the true statement is Damon used the subtraction property of equality in step 3.
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{Question 20} Please help! Need by tonight! Thanks :)
Answer:
y=-3/2x +2
Step-by-step explanation:
Answer:
y = 1.50x +2
Step-by-step explanation:
First, we must find two points.
(0, 2) --- > y-intercept (1, 0.5)Equation of a straight line:
y = mx + b ------(i)
Step 1: Calculating Slope (m).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-0.500}{1-0}[/tex]
[tex]m=\frac{1.50}{1}[/tex]
[tex]m=1.50[/tex]
Now putting value of m in equation (i)
y = 1.50x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (0,2) for calculating y-intercept:
y = mx + b2 = 1.50(0) + b
2 = 0 + b
2 = b
b = 2
Now putting value of b in equation (ii)
y = 1.50x + 2
Using point-slope form, write the equation of the line that passes through the point (−1,4) and has a slope of −3.
step by step explanation will give 100 points pls answer fast
Answer:
y - 4 = - 3(x + 1)Step-by-step explanation:
Point- slope formy - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the point on the lineGivenm = - 3,(x₁, y₁) = ( - 1, 4).Plug in to get the equation of the liney - 4 = - 3(x - (-1)) ⇒ y - 4 = - 3(x + 1)Answer:
Answer:
y - 4 = - 3(x + 1)
Step-by-step explanation:
Point- slope form
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the point on the line
Step-by-step explanation:
y=-2/5x-2 in stander form
Answer:
2x + 5y = -10
Step-by-step explanation:
Y = -2/5x - 2
5Y = 5(-2/5x - 2)
5Y = -2x - 10
2x + 5Y = -10
Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occur:
F(x)= - 3x² + 18x + 3
Select the correct choice below and fill in the answer boxes to complete your choice.
(Simplify your answers.)
The function has a maximum value of ___ at x=____.
The function has a minimum value of ____ at x=____.
The quadratic function has a maximum value of 0 at x = 3
Maximum and Minimum Value of Quadratic FunctionHere, the maximum value f(x) at x = 1 is called the absolute maximum value, global maximum or greatest value of the function f on the closed interval [0, 1]. Similarly, the minimum value of f(x) at x = 0 is called the absolute minimum value, global minimum or least value of the function f on the closed interval [0, 1].
In the function given f(x) = -3x² + 18x + 3
dy/dx = -6x + 18
For stationary values
0 = -6x + 18
6x = 18
x = 3
d²y/dx² = -6
for maximum or minimum value
d²y/dx² = -6x + 18
-6(3) + 18 = 0
The function has a maximum value of 0 at x = 3
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Please help :D I will give brainliest.
The Haddads expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85, but did not know by how much. Their
account showed a previous balance of $417.80, $350.00 in deposited checks,
an automatic deposit of $150.00, and $5.25 in interest. If the Haddads' present
balance is $555.82, by how much did this month's gas bill exceed last month's bill?
The gas bill exceeded $87 from last month to this month.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, The Haddad expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85 but did not know by how much.
Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.
∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.
Haddads' present balance is $555.82,
∴ The gas bill is $(858.69 - 555.82) = $302.87.
So the gas bill s exceeded by $(302.87 - 215.85) = $87.
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Which sequence of transformations can be used to show that triangle J is congruent to triangle P?
Answer:
it's answer D
Step-by-step explanation:
because it is the angle postulate theorem
Answer:
it's answer D
Step-by-step explanation:
Can someone help me I have to verify the trig identities.
We have proved the given trigonometric equations by using trigonometric identities.
What are the trigonometric identities?
Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the most important trigonometric identities. We'll need to apply the sine and cosine rules to non-right-angled triangles.
For the first equation:
The given equation is
[tex]sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx=sec^2(x)[/tex]
Now simplifying the given equation, we can write
[tex]LHA= sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx\\\\LHS=sec^2(x)-sec(x)cos(x)+\frac{sin(x)}{sin(x)}+\frac{cos(x)}{sin(x)}-cot(x)\\\\LHS=sec^2(x)-1+1+cot(x)-cot(x)\\\\LHS=sec^2(x)[/tex]
LHS = RHS.
Hence proved.
For the second equation:
cos(π - Θ) + sin(π/2 + Θ) = 0
LHS = cos(π - Θ) + sin(π/2 + Θ)
= -cosΘ + cosΘ
= 0
LHS = RHS
Hence, we have proved the given trigonometric equations by using trigonometric identities.
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Question 9(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Which of the following tables represents the proportional relationship for 6 cups of grape juice for every three fourths cup of rainbow sherbet?
Rainbow Sherbet (cups) 0.75 1.5 2.5
Grape Juice (cups) 6 8 10
Grape Juice (cups) 0.75 1.5 2.5
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 6 8 10
Rainbow Sherbet (cups) 0.75 1 1.25
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 0.75 1 1.25
Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 represents the correct relationship.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The proportional relationship for 6 cups of grape juice for every three-fourths cup of rainbow sherbet.
So, the ratio of grape to rainbow sherbet is 3/4 : 6 = 3 : 24.
Which is (24/3) = 8 times.
Now checking the options Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 is the correct relationship.
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1/3 .21= ?
1/6.21=?
(5.6). 1/8=?
1/4.(5.6)=?
Answer:
0.3115264797507,0.1610305958132,0.7,1.4
Please help me this is a chaos, im giving 20 points!!
The constant of proportionality that relates the quantities x and y is 2.25.
An equation that relates the quantities is, y = 2.25x.
What is constant of proportionality?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
1) From the given table,
4.5 / 2 = 2.25
11.25 / 5 = 2.25
15.75 / 7 = 2.25
2) The constant of proportionality that relates the quantities x and y is,
y / x = 2.25
3) An equation that relates the quantities is,
y = kx,
where, k is constant of proportionality.
Here, k = 2.25
Therefore,
y = 2.25x
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Mr. Harmon graded a Pre-Algebra test that he gave to his eighth-grade students. The results were 27 As, 54 Bs, 15 Cs, 3 Ds, and 1 F. What is the ratio of As to Ds in this class?
Find the product of (3 x 10 9) and (2 x 10 9). Write the final answer in scientific notation.
6 x 10 81
6 x 100 18
6 x 10 18
6 x 10 9
Answer:
6 x 10^18
Step-by-step explanation:
3 x 2 = 6
10^9 * 10^9 = 10^(9+9) = 10^18
PLEASE HURRY A scuba diver descends in the water at a rate of 18.5 feet per minute for 3.1 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 22 feet per minute for 2 minutes.
What is the scuba diver's position relative to sea level after the 5.1 minutes?
Enter your answer as a decimal in the box.
Answer: -13.35
Step-by-step explanation:
Trust the process
A first number plus twice a second number is 10. Twice the first number plus the second totals 26. Find the numbers.
The smaller of the two numbers is what?
Step-by-step explanation:
let the first number be x &
the second number be y
x+2y=10×2
2x+y=26×1
2x+4y=20
2x+y=26
subtract
3y=6
divide both sides by 3
3y/3 = 6/3
y=2
put y=2 in x+2y=10
x+2(2)=10
x+4=10
x=10-4
x=6
the smallest number is 2
How many permutations are there in BOOKKEEPING
Answer: There are 151200 permutations
Answer:
In the word "bookkeeping" there are approximately 151,200 permutations.
Step-by-step explanation:
Permutations:
Is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Find the product.
5.) 27.5 X 9 =
tan^2x+1=sec^2x
how do i prove the identity
The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.
How to prove a derivate trigonometric formula
In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.
Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:
sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x
Step 2 - Divide each side of the formula by cos² x:
sin² x / cos² x + cos² x / cos² x = 1 / cos² x
(sin x / cos x)² + 1 = (1 / cos x)²
Step 3 - Use the definition of the two trigonometric functions:
tan² x + 1 = sec² x
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find the missing terms of the arithmetic sequence __ -6 __ __ 15 __
The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
an = a1, a2, a3, a4, a5, a6
formula for nth term is :
an = a + (n - 1)d
where
an = last term
a = a1 = first term
n = number of terms
d = difference between two terms
here
a2 = a + d
- 6 = a + d ....(1)
a5 = a + 4d
15 = a + 4d .......(2)
on solving equation we get :
- 6 = a + d ....(1)
15 = a + 4d .......(2)
(-) (-) (-)
- 21 = - 3d
d = 21/3
d = 7
using the value of d in equation the value of a is :
- 6 = a + d
-6 = a + 7
a = -6 -7 = -13
then
a1 = a = -13
a2 = a + d = -13 + 7 = -6
a3 = a + 2d = -13 +2 x 7 = 1
a4 = a + 3d = -13 + 3 x 7 = 8
a5 = a + 4d = -13 +4 x 7 = 15
a6 = a + 5d = -13 +5 x 7 = 22
The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
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Dela made 21 peanut butter sandwiches with a 12-ounce jar of peanut butter.
How many ounces of peanut butter did Dela use on each sandwich? Use any strategy to solve this problem.
Answer:
Oh this is easy
Dela made 21
all of them is 12 ounce
so to know each of them
21/12
So the answer is 1.75ounce of peanut butter per sandwich
Step-by-step explanation:
I think i got it right
Solve x − 7y = 8 for x.
Answer:
x=7y+x
Step-by-step explanation:
Isolate x on one side
x-7y=8
+7y. +7y
x=7y+8
Hopes this helps please mark brainliest
