The mean of the sample means will be 25
As Sample mean is an estimate of the population mean. If we increment the number of observations the precision of the sample means will be improved to get closer to the population mean and according to Central Limit Theorem, The sampling distribution of the sample statistic can be considered roughly if any of the below-mentioned criteria is satisfied :
The sample measure is expansive or at the slightest 30. If the sample estimate is less than 30 at that point the distribution of the population from which the sample is chosen ought to be normal.We are provided with a sample size which is 100, a population mean which is 25, and a population standard deviation which is 20.
So , n =100
μ= 25
σ= 20
therefore, the mean of the sample means is
μₓ =μ
= 25
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Simplify. (a²b) ³.(b²c²)
Answer:
(a²b)³(b²c²)=a⁶b⁵c²
4. 14% of 81 is what number?
Answer:
11.34
Step-by-step explanation:
14% of 81 =
14% × 81 =
14/100 × 81 =
(14 ÷ 100) × 81 =
14 × 81 ÷ 100 =
1,134 ÷ 100 =
11.34
Identify the following fraction as a proper fraction or an improper fraction
16
11
The given number [tex]\frac{16}{11}[/tex] is an improper fraction.
What are improper and proper fractions?Proper fraction = A fraction with a smaller numerator than denominator is said to be a correct fraction. A fraction whose numerator is the same as or bigger than its denominator is said to be inappropriate. Proper fractions include 3/4, 2/11, and 7/19.
Improper fraction = A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.
When we divide 16 by 11 we get a quotient of 1 and a remainder of 5.
This fraction after solving can be represented as [tex]11\frac{1}{6}[/tex] which is a mixed fraction.
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What is an equation of the line through (0, -3) with slope of 2/5
Answer:
y = [tex]\frac{2}{5}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{2}{5}[/tex] and line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{2}{5}[/tex] x - 3 ← equation of line
Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Group of answer choices
Nico
Aditi
Erick
Raj
Sandra
By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.
How to solve the given equation?In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:
2/5(5 + x) = 8
Multiplying both sides by 5/2, we have:
5/2 × 2/5(5 + x) = 8 × 5/2
5 + x = 40/2
5 + x = 20
Subtracting 5 from both sides, we have:
5 + x - 5 = 20 - 5
x = 15
Method 2.In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:
2/5(5 + x) = 8
Multiplying both sides by 1/2, we have:
1/2 × 2/5(5 + x) = 8 × 1/2
1/5(5 + x) = 4
Multiplying both sides by 5, we have:
5 × 1/5(5 + x) = 4 × 5
5 + x = 20
Subtracting 5 from both sides, we have:
5 + x - 5 = 20 - 5
x = 15
Method 3.In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:
2/5(5 + x) = 8
2/5 × 5 + 2/5 × x = 8
2 + 2x/5 = 8
Subtracting 2 from both sides, we have:
2 - 2 + 2x/5 = 8 - 2
2x/5 = 6
Multiplying both sides by 5/2, we have:
5/2 × 2x/5 = 5/2 × 6
x = 30/2
x = 15.
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The line parallel to y=1/4x+1 that passes through the point (6,-2)
The equation for the line parallel to y=1/4x+1 that passes through the point (6,-2) is x-4y=14 as the slope for both lines are equal and using slope-point form of equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What is Slope-Point form?The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
The slope for the line will be 1/4 and the given points will be (6,-2) so the equation for the line is
y-y1=m(x-x1)
y+2=1/4(x-6)
4y+8=x-6
x-4y=14
Given that both lines have an equal slope and using the slope-point form of equation, the equation for the line parallel to y=1/4x+1 passing through the point (6,-2) is x-4y=14.
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A bookshelf is 31 3/4 inches wide 28 inch wide, binders on the shelf side-by-side how many binders can Maria place on the shelf?
The number of binder on the bookshelf is one
How to determine the number binders on the shelf?The given parameters are:
Width of the bookshelf = 31 3/4 inches
Width of the binders = 28 inches
From the question, we understand that the binders are stacked side by side
This means that the quotient of the width of the bookshelf and the width of the binder will give the number of binders
So, we have
Number of binders = Width of the bookshelf/Width of the binders
This gives
Number of binders = (31 3/4)/28
Evaluate the quotient
Number of binders = 1.13
Approximate
Number of binders = 1
Hence, there is only one binder on the bookshelf
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The temperature at 2 AM was -3°F is the temperature decreased 12°F and then increase 7°F what integer represents the new temperature?
The integer represents the new temperature is (-8) F.
what are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
Given:
At 2 a.m. temperature = -3F
Then temperature decreased 12°F = -12 F
and then increase 7°F = +7F
Now, the temperature is
= (-3) - 12 + 7
= -3 -5
=-8 F
Hence, the temperature is (-8) F
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The quadratic function − 0.379 ( x − 46 ) 2 + 2.62 ( x − 46 ) − 3.61 gives the percentage (in decimal form) of puffin eggs that hatch during a breeding season in terms of x , the mean sea surface temperature of the surrounding area, in degrees Fahrenheit.
a
.
What is percentage of puffin eggs that will hatch at
51°F? Round your answer to the nearest tenth of a percent.
b
.
For what mean temperature is the percentage of hatched puffin eggs a maximum? Round your answer to the nearest tenth of a degree.
°F
Find the percentage of hatched eggs at this temperature. Round your answer to the nearest tenth of a percent.
The percentage of puffin eggs that hatch given in decimal form by the quadratic function, f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61, gives;
a. At 51 °F, 1.5% of the eggs will hatch
b. The temperature at which the maximum percentage of puffin eggs will hatch is approximately 49.5 °F
The maximum percentage of eggs that hatch is approximately 91.8 %
What is a quadratic function?A quadratic function is a polynomial of the second degree (degree 2) such that the highest power of the variables in a quadratic function is 2
The quadratic function is presented as follows;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
Where;
f(x) = The percentage of the eggs that hatch
x = The mean sea surface temperature of the area in degrees Fahrenheit
a. The percentage of the eggs that will hatch at 51° is therefore;
f(51) = -0.379•(51 - 46)² + 2.62•(51 - 46) - 3.61 = 0.015
The percentage of the eggs that hatch at 51° d is f(51) = 0.015 × 100% = 1.5%
b. The temperature for which the percentage of hatched puffin eggs is a maximum, is given by the maximum value of the quadratic function as follows;
At the maximum value of the quadratic function, f(x) = a•x² + b•x + c, we have;
x = -b/(2•a)
Therefore, where we have;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
At the maximum value;
x - 46 = -2.62/(2×(-0.379)) = 1310/379
x = 46 + 1310/379 ≈ 49.5°Which gives;
The mean temperature at which the percentage of hatched puffin eggs is a maximum is approximately 49.5°Second part;
The percentage of eggs that hatch at the temperature that gives the maximum percentage of eggs is the maximum percentage of eggs, which is found as follows;
f(46 + 1310/379) = -0.379•(1310/379)² + 2.62•(1310/379) - 3.61 ≈ 0.9179683
The maximum percentage of puffin eggs is therefore;
f(46 + 1310/379) ≈ 0.9179683 × 100 ≈ 91.8%Learn more about quadratic functions here:
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5. Find the distance from the point (0, -3) to the line y = x - 1.
Distance from point (0, -3) to the line y = x - 1 = [tex]\sqrt{2}[/tex]
Given:
Point =(0,-3) => x = 0; y = -3
Line = y = x - 1 => a= 1, b= -1, c=-1
How is the distance from the point to the line calculated?
Let us consider the distance to be d,
[tex]d= \frac{ax+by+c}{\sqrt {a^{2}+b^{2}} } \\\\=\frac{1(0)-1(-3)-1}{\sqrt{2} } \\\\=\frac{2}{\sqrt{2} } = \sqrt{2}[/tex]
What is the distance from a point to a line?
The distance between a point and a line in Euclidean geometry is the shortest path between any two points on an infinite straight line. The length of the line segment connecting the point to the closest point on the line, measured perpendicularly to the line, is the distance between them.If the variances of the dependent and independent variables are equal, then Deming regression, a form of linear curve fitting, produces orthogonal regression, in which each data point's degree of fit error is expressed as the angle of the point from the regression line.To learn more about distance from a point to a line, refer:
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Does (-7,-7) make the equation y=x true
Answer: Yes it does.
Step-by-step explanation:
–3d = 5.7
ANSWER ASAP!!!!!!!!!!
Answer:
D = 1.9
You can find for d by using the associative property of division (divide instead of multiply):
5.7 divided -3 = 1.9
Step-by-step explanation:
Hope it helps! =D
600 people went to the basketball game on Friday and 14% of them bought popcorn. How many people bought popcorn at the basketball game?
Answer:
84 people
Step-by-step explanation:
14 percent means that for each 100, there are 14 of something.
This is the most common method to calculate 14% of 600. 600 is the Whole, 14 is the Percent, and the Part is what we are calculating. Below is the math and answer to "What is 14% of 600?" using the percent formula.
Percent Formula:
(Whole × Percent)/100 = Part
(600 × 14)/100 = 84
14% of 600 = 84
water is leaking from an inverted conical tank at a rate of . water is also being pumped into the tank at a constant rate. the tank has height and the diameter at the top is . if the water level is rising at a rate of when the height of the water is , find the rate at which water is being pumped into the tank. hint: let denote the rate (in ) at which the tank is being filled, and let denote the volume (in ) of water in the tank. then rate in - rate out , so it suffic
The rate of the water being pumped into the tank is 289,753 cm3/min
d = 4m
∴ r = 2m
h = 6m
Therefore r = h/3
The formula for the volume of the cone is:
V=(1/3)π•r2h
substitute:
V=(1/3)π (h/3)2h
V=(1/27)π h3
Derive both sides with respect to time:
dV/dt = (1/9) π h2• dh/dt
When h= 2 meters = 200 cm when dh/dt = 20
dV/dt = (1/9) π (200)2• (20)
dV/dt = (800,000/9) π ~ 279,252.68
Meaning the volume of water is increasing at a rate of 279,252.68 cm3/min.
However, it's leaking out at a rate of 10,500 cm3/min. Therefore the rate of the water being pumped into the tank is:
279,252.68 + 10,500 = 289,752.68 ~ 289,753 cm3/min
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a. write a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up. b. write a rule for congruence mapping that reflects a figure across the y-axis.c. why are these mappings called congruence mappings?
Given:
Two different congruency mapping
To find:
a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up
b) a rule for congruence mapping that reflects a figure across the y-axis
[tex]\begin{gathered} a)\text{ Translation rule to the right:} \\ f(x\text{ -d\rparen: \lparen x, y\rparen }\rightarrow\text{ \lparen x+d, y\rparen} \\ Translation\text{ rule up:} \\ f(x)\text{ + b: \lparen x, y\rparen }\rightarrow\text{ \lparen x, y + b\rparen} \\ \\ 5\text{ units to the right and 3 units up:} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ reflection across the y-axis} \\ The\text{ x coordinate will be negated while the x coordinate will remain constant} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ The mappings are called congruence mapping because the shapes and size remain the same } \\ \text{but the }position\text{ changes.} \\ As\text{ a result the corresponding angles and sides will be equal} \end{gathered}[/tex]question 1 and 2 (10 popints)
Exponential function:
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given,
The exponential function = 14²The value of this exponential function :
14 × 14 = 196
The exponential function = 4⁵The value of this exponential function :
4 × 4 × 4 × 4 × 4 = 1024
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If a space rover has a mass of 3900 kg, then what is its weight on Mars?
Answer:
Weight on Mars: 1,475.32 kg
Step-by-step explanation:
The formula is Weight on Mars= (Weight on Earth/9.81m/s2) * 3.711m/s2.
If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.
What is Mass?Mass is a dimensionless quantity representing the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram.
Given,
The mass of a space rover is 3900 kg.
We need to check what is its mass in Mars.
The mass of space rover in Mars will also be same 3900 kg because the mars is same quantity it wont change according to place or time, it remains constant. Where as weight would be changed.
The mass of the object is always constant, anywhere it is on the Earth or Moon or any other planet.
Hence, If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.
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An airline company wants to provide service to San Francisco, Los Angeles, Chicago, Dallas, Washington D.C., and New York City. The company's president draws lines between each pair of cities in the list on a map. No three of the cities are collinear How many lines did the president draw?
The president draw 15 lines on map.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
here, it is given that :
there are 6 cities
No three of the cities are collinear that is are not in a straight line.
Now, to find the lines did the president draw use the formulae :
n(n-1)/2
where, n = number of cities
lines did the president draw = 6 x 5/ 2
= 15
Therefore, The president draw 15 lines on map.
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Which is equivalent to
Answer:
[tex]\frac{2y^5}{x^6}[/tex]
you have chosen the correct answer
6-8 7-12 1-4 0-1 find the value of these cards and put them in order from lowest to highest
The order from lowest to highest is -5, -3, -2, -1 .
What is ascending order ?
Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
6-8=-2
7-12=-5
1-4=-3
0-1=-1
Order : -5, -3, -2, -1
Avoid becoming confused by the values following the negative sign. The value of a number decreases with increasing size after a negative sign.
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A gym employee earns the same amount each month. After working for three months, he earned $4,500. Complete the table to determine how much money he will make over a five-month period. how much will he earn after working 1 month?
1. The money that the gym employee earns in 1 month is $1500.
2. The money that the gym employee earns in 5 months is $7500.
How to calculate the value?The gym employee earns the same amount each month and after working for three months, he earned $4,500.
In this case, the amount that he earns monthly will be:
= Total amount / Number of months
= $4500 / 3
= $1500
He earns $1500 monthly.
The money that the gym employee earns in 5 months will be:
= 5 × $1500
= $7500.
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NEED HELP ASAP. GETS BRAINIEST GET A 100 POINTS
Is the Fibonacci sequence arithmetic, geometric, or neither? Explain how you know.
Look at quotients . What do you notice about this sequence of numbers?
The 15th through 19th Fibonacci numbers are 610, 987, 1597, 2584, 4181. What do you notice about the quotients ?
Answer:
there are different kind of sequence number and just multiply the fractions.
Step-by-step explanation:
multiply fractions aND you will get the answer.
Creating equivalent ratios
12:___=16:24
The equivalent ratio is 12: 18
The ratio is 12:_ = 16: 24
12/x = 16/ 24
x≠0, because the denominator can never be 0.
Solve the equation
12/x = 16/24
12/x = 2/3
x = 18
Therefore the equivalent ratio is 12:18.
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Which relation is a function?
Answer:
option C
Step-by-step explanation:
due to the vertical line test it only passes through the x point once
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
d
Step-by-step explanation:
because you're already given the hypotenuse "c" and a side length "a"
so
8^2+ y^2=12^2
Which multiplication problem can be used to determine how many possible combinations there are for a lock consisting of 3 digits from 0–9, if the digits can be repeated?
___________________
900
___________________
Given: A = [ 1 -1 -2 3] B = [ 1 5 8 -8 ] C = [ 1 2 3 4 ]
Solve: AX + B = C
Given in the question the matrix
A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
Given A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
find x, if AX + B = C
AX + B = C
AX = C -B = [ 1 2 [ 1 5
-
3 4] 8 -8 ]
AX = [ 1-1 2-5 = [ 0 -3
3-8 4+8 ] -5 12]
X = A -1 [ 0 -3
-5 12] .........(i)
A = [1 1 |A| = {3*1 - 1 *(-2)}
-2 3] = 5
A-1 = [tex]\frac{adj A}{|A|}[/tex]
Adj A = [cofactor A]^1 = [ [tex]a_{11}[/tex] = 3 [tex]a_{12}[/tex] = 2
[tex]a_{21}[/tex] = -1 [tex]a_{22}[/tex] = 1 ] ^1
adj A = [ 3 -1 A -1 = 1/5 [ 3 -1
2 1] 2 1]
x = 1/5 [3 -1 [ 0 -3
2 1] -5 12]
= 1/5 [ 5 -21 = [ 1 -21/5
-5 8] -1 8/5] ..........(ii)
Hence, required solution of the given matrix is equation (ii)
Therefore, Given the matrix A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
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Por favor ayúdenme no sé cómo hacer esto
1. The value of x in the triangle is B. 22.5°.
2. The value of x in the triangle is B. 22.5°.
3. The value of the limit illustrated is D. 32
How to calculate the value?1. It should be noted that the total angle in a triangle is 180°. The three angles given are illustrated as:
Angle 1 = 3x
Angle 2 = x + 30°
Angle 3 = 180° - 120° = 60°
The value of x will be:.
3x + x + 30 + 60 = 180
4x + 90 = 180
4x = 180° - 90°
4x = 90°
x = 90/4.
x = 22.5°
2. Note that the question was repeated. Therefore, the answer is illustrated above The value of x is 22.5°.
3. x³ + 7x² - 4
when x = 2
x³ + 7x² - 4
= 2³ + 7(2)² - 4
= 8 + 28 - 4
= 32
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Need help! please explain how you got the answer as well please and thank u <3
44 points till b givin
Answer:
C. between 14.1 and 14.2
Step-by-step explanation:
√100 × 2
√(10 × 10) × 2
10√2 = 14.14
I hope this helps!
Answer:
C. Between 14.1 and 14.2
10√2 ≈ 14.142135624
Step-by-step explanation:
Help with this question asap please help
The meaning of vertical intercept in this context can be inferred from the options to mean that the helicopter took off from a height of 50 ft.
What is the vertical intercept?In a linear problem or a graph, the vertical intercept, which is also known as the y-intercept, refers to the value of y when the value of x is 0.
Assuming y in this problem refers to the height and x refers to the minutes, the vertical intercept would be the height at 0 minutes.
If the vertical intercept is 50 ft then it means that the helicopter took off from 50 feet because at takeoff, the value of x would be 0 minutes.
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