The value of x has a z-score of three is 20
How to determine the value of x?The given parameters are:
Mean = 2
Standard deviation = 6
z = 3
The z-score is calculated as:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]3 = \frac{x -2}{6}[/tex]
Multiply through by 6
18 = x - 2
Add 2 to both sides
x = 20
Hence, the value of x has a z-score of three is 20
Read more about z-score at:
https://brainly.com/question/15016913
#SPJ1
please help me important question in image
Segment BF is 36 will be the accurate statement.
Similarity theorem of triangleA triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.
From the given triangle, the following expression is true:
EC/FC = AC/BF+FC
Substitute the given parameters into the formula to have:
20/30 = 24+20/BF+30
20/30 = 44/BF+30
2/3 = 44/BF + 30
2(BF+30) = 132
2BF + 60 = 132
2BF = 132 - 60
2BF = 72
BF = 36
Hence the correct statement will be that segment BF is 36
Learn more on similar triangle here:
#SPJ1
Find the greatest common factor of 21x^4 and 49x^3
The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to 7x³.
To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.
To find the factors, we can break each term down into its prime factors:
21x⁴ = 3 * 7 * x * x * x * x
49x³ = 7 * 7 * x * x * x
The common factors are 7 and x³. To find the GCF, we multiply these common factors together:
GCF = 7 * x³
GCF = 7x³
To learn more about greatest common factor click on,
https://brainly.com/question/9767511
#SPJ1
What is the ratio for 3 rectangles and 4 ovals in its simplest form?
The ratios for the rectangles and the ovals is 4 : 3
Calculating the ratios for the rectangles and the ovalsFrom the question, we have the following parameters that can be used in our computation:
Rectangle = 4
Oval = 3
The ratio can be represented as
Ratio = Rectangle : Oval
When the given values are substituted in the above equation, we have the following equation
Rectangle : Oval = 4 : 3
The above ratio cannot be further simplified
This means that the ratio expression would remain as 4 : 3
Hence, the solution is 4 : 3
Read more about ratio at
https://brainly.com/question/12024093
#SPJ1
Write the coordinates of the vertices after a dilation with a scale factor of 1 2 , centered at the origin.
The coordinates of the vertices after a dilation of the scale factor would be:
W' = (2.5, 5)V' = (0, -5)U' = (2.5, -5)How to dilate the vertices ?To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.
Given the vertices:
W = (5, 10)
V = (0, -10)
U = (5, -10)
After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:
W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)
V' = (0 * 1/2, -10 x 1/2) = (0, -5)
U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)
Find out more on dilation at https://brainly.com/question/20482938
#SPJ1
Find the distance between (2, 5) and (-5, 8).
58
√58
2√43
2
Answer:
d = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )
d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]
= [tex]\sqrt{(-7)^2+3^2}[/tex]
= [tex]\sqrt{49+9}[/tex]
= [tex]\sqrt{58}[/tex]
There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
The ratio is 3:7
Step-by-step explanation:
You add 104+78
The un-simplified ratio is 78:182
hope this helps!!
rate this if it does!
A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
To learn more about rectangle click on,
https://brainly.com/question/19127628
#SPJ1
how many cubes that are 1" x 1" x 1" could fit into a box that is 8" x 8" x 8"
Answer:
512
Step-by-step explanation:
To determine how many 1" x 1" x 1" cubes can fit into an 8" x 8" x 8" box, we need to calculate the volume of the box and then divide it by the volume of a single cube.
The volume of the box is calculated by multiplying its length, width, and height:
Volume of the box = 8" x 8" x 8" = 512 cubic inches.
The volume of a single cube is 1" x 1" x 1" = 1 cubic inch.
To find out how many cubes can fit, we divide the volume of the box by the volume of a single cube:
Number of cubes = Volume of the box / Volume of a single cube
Number of cubes = 512 cubic inches / 1 cubic inch
Number of cubes = 512
Therefore, 512 cubes that are 1" x 1" x 1" can fit into an 8" x 8" x 8" box.
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answer: where is the answer choices
Step-by-step explanation:
Please solve this question
The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.
We have,
The vertex form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
Now,
Given that the parabola passes through (-2, 4) and has a vertex (0, 8), we can substitute these values into the equation to find the value of 'a'.
Using the vertex (0, 8):
8 = a(0 - 0)² + 8
8 = a(0) + 8
8 = 8
Since the coefficient of the squared term is 'a', which remains unchanged, we can conclude that a = 1.
Therefore,
The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.
Learn more about parabola here:
https://brainly.com/question/21685473
#SPJ1
HELP PLEASE ASAP PHOTO INCLUDED
The volume of water that the pool can hold is 150.72 cubic centimeters.
How to find the volume of the pool?Remember that the volume of a cylinder of radius R and height H is:
V = pi*R²*H
Where pi = 3.14
For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft
Replacing that in the volume formula we will get:
V = 3.14*(4cm)²*3cm
V = 150.72 cubic centimeters.
Learn more about cylinders at:
https://brainly.com/question/9554871
#SPJ1
Please someone help me with this. Simplify. The expression in the picture no negative exponents should be added in the answer
A simplification of the given expression is 1/m¹⁶.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:
[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]
1/m¹⁶
Read more on exponent here: brainly.com/question/27858496
#SPJ1
The side of a square is measured to be 16 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer.
The estimated error in the calculated area is approximately 3.2ft²
How did we estimate the error?To estimate the error in the calculated area of a square, use linear approximation or differentials.
The area of a square is given by the formula A = s², where s represents the length of a side.
Calculate the area of the square using the given side length of 16 ft:
A = (16 ft)²
A = 256 ft²
Now, let's consider the possible error in the side length, which is ±0.1 ft. Treat this error as a change in the side length (Δs) and use linear approximation or differentials to estimate the corresponding change in the area (ΔA).
Using linear approximation, express the change in the area as:
ΔA ≈ 2s Δs
Substituting the values:
ΔA ≈ 2(16 ft)(0.1 ft)
ΔA ≈ 3.2 ft²
Therefore, the estimated error in the calculated area is approximately 3.2ft².
learn more about area of a square: https://brainly.com/question/11444061
#SPJ1
Given: KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
Prove:
An incomplete flowchart proof is shown.
By ASA congruency triangle KBH is congruent to triangle NWH.
Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
From the given figure,
Consider ΔKBH and ΔNWH,
∠KHB=∠NHW (Vertically opposite angles)
∠HKB=∠HWN (Interior alternate angles parallelogram)
KH=HW (Diagonals bisect each other)
By ASA congruency ΔKBH ≅ ΔNWH
Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.
To learn more about the congruent theorem visit:
https://brainly.com/question/24033497.
#SPJ1
I just need the answer for letter b
If f(x) = 1/343, then x = -3. The point on the graph of f when f(x) = 1/343 is (-3, 1/343).
How to explain the valueA point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate.
If f(x) = 1/343, then x = -3. This is because 343 = 7³, therefore the inverses is 1/343. The point on the graph of f when f(x) = 1/343 is (-3, 1/343
Learn more about graph on
https://brainly.com/question/19040584
#SPJ1
You deposit $5000 in an account earning 3% interest compounded continuously. How much will you have in the
account in 15 years?
Answer:
$7841.56----------------------
Use the compound interest formula:
[tex]A = Pe^{rt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 3% = 0.03;t = time period in years = 15.Plugging in the values, we get:
[tex]A = 5000*e^{0.03*15}[/tex][tex]A = 7841.56[/tex]increase a gross by 10%
The results of increasing a gross by 10% is 158.4.
What is percentage?Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.
In mathematics, gross is written in figures as 144
increase a gross by 10%
= 144 + (10% × 144)
= 144 + (0.1 × 144)
= 144 + 14.4
= 158.4
Hence, 158.4 is the 10% increase in gross.
Complete question:
Calculate the increase in a gross by 10%.
Read more on percentage:
https://brainly.com/question/843074
#SPJ1
Does the data follow a normal distribution? Why or why not?
Find the quotient and express the answer in scientific notation. 302 ÷ (9.1 x 10^4 )
The quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]
How to find the quotientDividing 302 by 9.1 gives:
302 ÷ 9.1 ≈ 33.1868131868
Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:
33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]
Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]
Learn more about quotient at https://brainly.com/question/11995925
#SPJ1
factorise fully
1) 3x² - 27y²
2) 2014² - 2013²
please help
Answer: 3x² - 27y² = (3x²) - (27)(y²) = 3(x² - 9y²) = 3(x - 3y)(x + 3y), and 2014² - 2013² = (2014 + 2013)(2014 - 2013) = (3127)(1) = 3127
Im not 100% sure of this answer cause I'm not that good at stuff like this but I still think this is right fr fr
A thermometer reading 10°C is brought into a room with a constant temperature of 36°C. if the thermometer reads 14°C after 2 minutes, what will it read after beint left in the room for 4 minutes? and for 9 minutes?
Answer:
4 minutes: 17.4 °C9 minutes: 23.7 °CStep-by-step explanation:
You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.
Newton's law of coolingNewton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...
T = 36 -26·(22/26)^(t/2)
At times of t=4 and t=9, the temperature readings will be ...
4 minutes: 36 -26(11/13)^(4/2) ≈ 17.4 °C9 minutes: 36 -26(11/13)^(9/2) ≈ 23.7 °C__
Additional comment
The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.
<95141404393>
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
The probability that it is raining if the flight has been delayed is 0.07, or 7%.
How to calculate the probabilityWe can use the following formula to calculate the probability that it is raining if the flight has been delayed:
P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)
We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):
= 0.07 * 0.18
= 0.0126.
Substituting these values into the formula, we get:
P(Rain|Delayed) = 0.0126 / 0.18 = 0.07
Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.
Leans more about probability on
https://brainly.com/question/24756209
#SPJ1
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The proof of ΔRUV ≅ ΔSUT is shown below.
Given that:
RSTV is a rectangle and U is the midpoint of VT.
Here, We have to Prove:
⇒ ΔRUV ≅ ΔSUT
Now, We can prove as;
Statement Reason
1) RSTV is a rectangle Given
2) Angle V and T are Because every angle in a rectangle is 90
right triangle.
3) ∠V ≅ ∠T Because both are right angle.
4) U is the midpoint of VT. Given
5) VU = UT By midpoint theorem.
6) VR ≅ TS Opposite sides of rectangle.
7) ΔRUV ≅ ΔSUT By SAS congruency theorem.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
Please urgent help I can’t figure this out thank you guys for always helping
Answer:
Domain: {-24, -12, -8, 9, 14, 50}
Range: {23, 69, 83, 92, 97, 32}
Step-by-step explanation:
The domain of a function is the set of all possible input values (usually x) for which the function is defined. The range of a function is the set of all possible output values (usually y, which is synonymous with f(x)) that the function can produce.For a function like f(x), each coordinate is in the form (x, f(x)) aka (x, y)
Since our x-coordinates are -24, -12, -8, 9, 14, and 50, the domain of f(x) is {-24, -12, -8, 9, 14, 50}
Since our f(x) or y-coordinates are 23, 69, 83, 92, 97, and 32, the range is {23, 69, 83, 92, 97, 32}
Esther ran round the playground and 12 times. The playground is 240 m by 160 m. what distance did she cover?
The total distance she cover after running is 9600 meters
How to calculate the total distance she cover?From the question, we have the following parameters that can be used in our computation:
Number of times = 12 times
Dimensions of the playground = 240 m by 160 m
The perimeter of the playground is calculated as
Perimeter = 2 * sum of dimensions
substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (240 + 160)
The total distance she cover is calculated as
total distance = 12 * 2 * (240 + 160)
Evaluate
total distance = 9600 meters
Hence, the total distance she cover is 9600 meters
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
make a table for each equation using the following numbers as : x -2,-1,0,1
y=3x-2
The equation y = 3x - 2. can be placed in table as shown below. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
In this table, each row represents a pair of values (x, y) that satisfy the equation y = 3x - 2. For example, when x is -2, y is calculated as 3(-2) - 2 = -8. Similarly, for the other values of x, the corresponding values of y are calculated accordingly.
Here's a table showing the values of x and the corresponding values of y for the equation y = 3x - 2:
x y
-2 -8
-1 -5
0 -2
1 1
To fill in the table, substitute each value of x into the equation and calculate the corresponding value of y. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
For more such questions on equation , Visit:
https://brainly.com/question/29174899
#SPJ11
On a standardized exam, the scores are normally distributed with a mean of 300 and
a standard deviation of 40. Find the z-score of a person who scored 280 on the exam.
Answer:
Submit Answer
Privacy Policy Terms of Service
attempt 1 out of 2
The z- score of a person who scored 280 on the exam can be found to be - 0. 5.
How to find the z - score ?A z-score indicates how many standard deviations an element is from the mean.
The formula is:
Z = ( X - μ ) / σ
The details here are:
X = 280, μ = 300, and σ = 40
The z - score is therefore :
Z = (280 - 300) / 40
= -20 / 40
= -0.5
In conclusion, the z - score of a person who scored 280 on the exam is -0.5. This means that their score is half a standard deviation below the mean.
Find out more on z - score at https://brainly.com/question/31018061
#SPJ1
geometry need help please
The record low temperature in Fargo, ND is -35 degrees. The record high is 114 degrees. What is the difference in the record high and the record low temperatures?
The difference between the record high and low temperatures is 149 degrees.
What is the difference between the temperatures?A negative number is a number that is less than zero. A negative number usually has a minus sign in front of it. An example of a negative number is -35. A positive number is a number that is greater than zero. An example of a positive number is 10.
In order to find the difference between two or more numbers, subtract the numbers from each other.
Difference between the temperature = record high temperature - record low temperature
114 - -35
114 + 35 = 149 degrees
To learn more about subtraction, please check: https://brainly.com/question/854115
#SPJ1
What’s the constant term of the polynomial 2x^3-5x^2+8*x+3
The constant term of the polynomial 2x³-5x²+8x+3 is 3.
A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.
The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.
The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.
Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.
To know more about polynomials follow
https://brainly.com/question/29804635
#SPJ1