The area between z = -1.71 and z = 0.08 is 0.4883, in median .
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.
=> P(-1.71 < Z < 0.08 ) = P(Z < 0.08 ) - P(Z < -1.71)
= 0.5319 - [1 - P(Z < 1.71)]
= 0.5319- [1 - 0.9564]
= 0.4883
Hence, the area between z = -1.71 and z = 0.08 is 0.4883.
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Explain the five properties of multiplication.
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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1/3 .21= ?
1/6.21=?
(5.6). 1/8=?
1/4.(5.6)=?
Answer:
0.3115264797507,0.1610305958132,0.7,1.4
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
6. ΔABC ≅ ΔYWZ
x=___ AC= ____ T=____ WZ= ___ WY=____
AB=____ m
7. ΔABC ≅ Δ ZYW
X=___ YZ=____ T=____ WZ=___ WY=___
6) The missing angles and lengths are; x = 14, T = 14, AB = WY = 60
7) The missing angles and lengths are; X = 7, ∠A = ∠Z =31°, T = 9, YZ = AB = 28
How to interpret congruent triangles?6) We are told that;
ΔABC ≅ ΔYWZ
That means triangle ABC is congruent to triangle YWZ
Thus;
∠C ≅ ∠Z
5x - 4 = 66
5x = 70
x = 14
Similarly, AB = WY
5T - 10 = 4T + 4
5T - 4T = 10 + 4
T = 14
AB = 5(14) - 10
AB = 60 = WY
7) We are told that;
ΔABC ≅ ΔZYW
That means triangle ABC is congruent to triangle ZYW
Thus;
∠A ≅ ∠Z
5X - 4 = 3X + 10
2X = 14
X = 7
∠A = 5(7) - 4 = 31° = ∠Z
Similarly;
2T + 10 = 4T - 8
T = 18/2
T = 9
YZ = 4(9) - 8
YZ = 28 = AB
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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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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?
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.
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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Find the product.
5.) 27.5 X 9 =
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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Find the volume of a right circular cone-shaped building with a radius of 3cm and a height of 14 cm.
The volume of the right circular cone is, 131.95 cubic centimeter.
What is cone?
A cone is a smooth-tapering three-dimensional geometric object with a flat base and an apex or vertex. The base of a cone is made up of all the points on a plane other than the apex, and the apex is connected to all the other points on the base by a series of line segments, half-lines, or lines.
Here, the radius, r = 3 cm, and height h = 14 cm.
We have to find the volume of right circular cone.
Since,
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]V = \pi (3)^3(\frac{14}{3})\\ V = \pi (3)(14)\\V = 42\pi \\V = 131.95 cm^3[/tex]
Hence, the volume of the right circular cone is, 131.95 cubic centimeter.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height as determined from the given information is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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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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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:
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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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%.
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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Solve the formula for t.
V=6πrt+7πr*2
t=
The unknown variable t has a value of t = (V - 7πr²)/6πr
How to determine the unknown variable?From the question, we have the following parameters that can be used in our computation:
Formula; V = 6πrt+7πr*2
Rewrite the formula properly
So, we have the following representation
V = 6πrt + 7πr²
Subtract the expression 7πr² from both sides of the equation
So, we have
V - 7πr² = 6πrt + 7πr² - 7πr²
Evaluate the difference
V - 7πr² = 6πrt
So, we have
6πrt/6πr = (V - 7πr²)/6πr
Evaluate
t = (V - 7πr²)/6πr
Hence, the value is t = (V - 7πr²)/6πr
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Answer:
[tex]t = \dfrac{V-7\pi r^2}{6\pi r}[/tex]
Step-by-step explanation:
V = 6πrt + 7πr²
Subtract the term without t from both sides.
V - 7πr² = 6πrt
Now you have a single term with t on the right side and two terms without t on the left side.
Switch sides.
6πrt = V - 7πr²
Divide both sides by 6πr.
[tex] t = \dfrac{V - 7\pi r^2}{6\pi r} [/tex]
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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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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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
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:
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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{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
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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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
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!
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
Please help :D I will give brainliest.
