The probability is approximately 0.8185 or 81.85%.
What is normal distribution?Normal distribution, also known as Gaussian distribution, is a probability distribution that is commonly used in statistics, mathematics, and the natural sciences to describe real-valued random variables whose distributions are not known.
To find the probability that a randomly selected x-value from a normal distribution with a mean of 48 and a standard deviation of 7 is between 34 and 55, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
For x = 34:
z = (34 - 48) / 7 = -2
For x = 55:
z = (55 - 48) / 7 = 1
We can use a standard normal distribution table or a calculator to find the area under the standard normal distribution curve between z = -2 and z = 1. This area represents the probability that a randomly selected x-value from the given normal distribution is between 34 and 55.
Using a standard normal distribution table, we can find the probabilities as follows:
P(z < -2) = 0.0228 (from the table)
P(z < 1) = 0.8413 (from the table)
Therefore, the probability that a randomly selected x-value from the given normal distribution is between 34 and 55 is:
P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185
So, the probability is approximately 0.8185 or 81.85%.
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Someone help me with these 3 math problems.
1. The value of the variable 'x' is 10 that is written as x = 10.
2. The equation is ∠3 + ∠4 = 90°. Then angles ∠3 and ∠4 will be complementary angles.
3. The measure of angle ∠2 is 60° which is an acute angle.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
1. ∠1 = 6x + 45 and ∠3 = 9x + 15
Angle ∠1 and angle ∠3 are opposite angles. Then the equation is given as,
∠1 = ∠3
9x + 15 = 6x + 45
9x - 6x = 45 - 15
3x = 30
x = 30 / 3
x = 10
2. Angle ∠2, angle ∠3, and angle ∠4 are supplementary angles. Then the equation is given as,
∠2 + ∠3 + ∠4 = 180°
90° + ∠3 + ∠4 = 180°
∠3 + ∠4 = 90°
3. Angle ∠1 is 120°, then the measure of angle ∠2 is given as,
∠1 + ∠2 = 180°
120° + ∠2 = 180°
∠2 = 60° (acute)
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As a landscaper, you are treating a client’s lawn with fertilizer. To prepare the correct amount of fertilizer, you need to know the area of the lawn. You measure the length of the rectangular lawn to be 37 feet and the width to be 21 feet.
What is the area of the lawn to the nearest square foot?
58
116
389
777
800
the the percent change from 50 to 22
Answer:
227.27%
Step-by-step explanation:
Max is finding the perimeter of different-sized equilateral triangles.
The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.
What is constant of proportionality?The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.
For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.
Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.
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Find
Domain:
Range:
x-intercept:
Y-intercept:
Horizontal Asymptote:
Vertical Asymptote:
For =1/x
Pic attach below
Answer:
Ignore my handwriting loll
Step-by-step explanation:
Hope this helps! :)
What number a is 24% of 25?
Answer: 24 percent of 25 is 6.
Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.
A parabola can be drawn given a focus of (1, 11)(1,11) and a directrix of y=3y=3. Write the equation of the parabola in any form.
The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.
what is parabola ?A parabola is a U-shaped curve in mathematics that is produced by the graph of a quadratic function. It is a particular kind of conic section, which is a circle made when a plane and a cone cross each other. A quadratic function with the following standard form can depict a parabola: Y = ax2+bx+c where are constants a, b, and c. Which way the parabola expands depends on the sign of the coefficient a.
given
We can use the following formula to express the equation of a parabola given a focus and a directrix:
where (h,k) is the parabola's vertex, p is the separation between it and the centre, and the directrix is represented by the horizontal line y = k - p.
The centre in this instance is (1,11), and the directrix is y=3.
We also understand that p is the distance, in this instance 4 units, between the vertex and the focus (since the focus is 4 units above the vertex). Therefore, we can enter the numbers into the formula to obtain:
(x - 1)^2 = 4(4)(y - 7) (y - 7)
The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.
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7/25 equivalent in percents
The larger rectangle is dilated to form the smaller rectangle. What is the scale factor?
Classify the dilation.
A. 5:1, enlargement
B. 5:1, reduction
C. 1:5, enlargement
D. 1:5, reduction
E. I don't know or I'm still thinking.
A
15
20
D
F3 G
E H4
The scale factor of the dilation is (d) 1 : 5 reduction
How to determine the scale factor dilationFrom the question, we have the following parameters that can be used in our computation:
The larger rectangle is dilated to form the smaller rectangle
Using the above as a guide, we have the following:
Larger rectangle = 5
Smaller rectangle = 1
So, we have
Scale factor = Smaller rectangle : Larger rectangle
Substitute the known values in the above equation, so, we have the following representation
Scale factor = 1 : 5
Hence, the scale factor is 1 : 5 reduction
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Mr. Perez ask Monica to measure the dimensions of the aquarium to see whether it could fit on the table S applied Michael measured the aquarium's left hand with angle at 96CM and 60CM respectively what is the area of the base of the aquarium
Therefore, the area of the base of the aquarium is 5760 square centimeters.
What is area?Area is a measure of the amount of space inside a two-dimensional (2D) shape or figure. It is usually measured in square units, such as square meters (m²) or square centimeters (cm²). The area of a shape is calculated by multiplying the length of one side or dimension of the shape by the length of another side or dimension. The resulting value represents the total number of square units that are contained within the shape. Area is an important concept in mathematics and is used in various fields, such as geometry, physics, and engineering. It helps in measuring and comparing the sizes of shapes and figures, and in determining how much material is needed to cover or fill a certain area.
Here,
The area of the base can be calculated using the dimensions of the aquarium.
Let's assume that the aquarium has a rectangular base with length L, width W, and height H. Then, the area of the base of the aquarium can be calculated as:
Area of base = Length x Width = L x W
If Monica measured the length and width of the base, we can use those measurements to calculate the area of the base. If not, we'll need to make additional assumptions or measurements.
Assuming we have the length and width of the base, we can calculate the area as follows:
Area of base = Length x Width
Area of base = 96 cm x 60 cm
Area of base = 5760 cm²
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Can you pls solve? Thanks
Answer:
[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]
Step-by-step explanation:
We have the following functions
[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]
1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]
First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]
Substitute this value for x in r(x)
[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]
So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]
2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]
First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]
Substitute this value for x in q(x)
[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]
The compositions of functions are:
(r o q)(4) = 5(q o r)(4) = 13How to find the compositions of the functions?Here we have the two functions:
q(x) = x² + 4
r(x)= √(x + 5)
We want to find the two compositions:
(r o q)(4) = r(q(4))
First let's find:
q(4) = 4² + 4 = 16 + 4 = 20
Then:
r(q(4)) = r(20) = √(20 + 5) = 5
And the other composition is:
(q o r)(4) = q(r(4))
First, r(4) = √(4 + 5) = 3
Then:
q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13
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The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=
The central angles for each category are approximately: Red: 100°, Blue: 150°, Green: 50° and Purple: 60°
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
To find the central angle of each category, we first need to calculate the total number of people:
Total = 20 + 30 + 10 + 12 = 72
Next, we can calculate the percentage of people who prefer each color:
Red: 20/72 = 0.278, or 27.8%
Blue: 30/72 = 0.417, or 41.7%
Green: 10/72 = 0.139, or 13.9%
Purple: 12/72 = 0.167, or 16.7%
To find the central angle for each category, we can multiply the percentage by 360°:
Red: 0.278 × 360° = 100.08°
Blue: 0.417 × 360° = 150.12°
Green: 0.139 × 360° = 50.04°
Purple: 0.167 × 360° = 60.48°
Therefore, the central angles for each category are approximately:
Red: 100°, Blue: 150°, Green: 50° and Purple: 60°
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The probability of a student taking a statistics class is 0.83, and the probability of a student taking a calculus class and a
statistics class is 0.66. What is the probability of a student taking a calculus class given that the student takes a statistics
class?
Round your answer to three decimal places.
Answer:
Step-by-step explanation:
We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:
P(calculus | statistics) = P(calculus and statistics) / P(statistics)
We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.
Substituting the values we have:
P(calculus | statistics) = 0.66 / 0.83
Simplifying the fraction:
P(calculus | statistics) = 0.795
Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.
0.004 divided by
0.24
Answer:
0.0166666666666666666666666666666666666666666667
Step-by-step explanation:
USE CALCULATORRRRRR
if x = 5 what is the value of 2x - 5
Answer:
answer is 5
Step-by-step explanation:
2x=5×2
so 2x=10
10-5=5
so 2x-5=5
Answer:
5
Step-by-step explanation:
2x - 5 first, substitute
2(5) - 5 then, multiply
10 - 5 = 5
The diagram shows Triangle ABC. What is the height of Triangle ABC? Show your work.
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as,
H² = P² + B²
The height of Triangle ΔABC is given as,
17² = h² + 15²
289 = h² + 225
h² = 289 - 225
h² = 64
h = 8 units
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
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Please I need help. I don’t understand this.
Answer: πr2h
= π×282×34
= 26656π
= 83742.29377409 centimeters3
Step-by-step explanation:
Answer:
The volume of the composite figure is 12,719 cm³ to the nearest whole number.
Step-by-step explanation:
The composite figure is composed of a cone and a half-sphere.
To calculate the volume of the figure, sum the volume of the cone and the volume of the half-sphere.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]
Therefore, the equation for the volume of the composite figure is:
[tex]V=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]
From inspection of the given diagram:
d = 28 cmh = 34 cmπ ≈ 3.14As the diameter of a circle is twice its radius, r = 14 cm.
Substitute the values of r, h and π into the equation and solve for V:
[tex]\begin{aligned}\implies V&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (3.14) (14)^2 (34)+\dfrac{2}{3} (3.14) (14)^3\\\\&=\dfrac{1}{3} (3.14) (196) (34)+\dfrac{2}{3} (3.14) (2744)\\\\&=6974.98666...+5744.10666...\\\\&=12719.09333...\\\\&=12719\;\sf cm^3\;\;(nearest\;whole\;number)\end{aligned}[/tex]
Therefore, the volume of the composite figure is 12,719 cm³ to the nearest whole number.
Triangle ABC, below, is a right triangle with the right angle at C. The measure of angle A is 34°. What is the measure of angle B?
15 POINTS!!! PLEASE HELPPP!!!
1. A hot piece of meat is removed from an oven and its surface temperature
is given by the formula S(t) = 72 +238•0.97^t, in degrees Fahrenheit, at time t
minutes after it was removed.
(a) What was the initial surface temperature of the meat?
I am not understanding how to do this at all could someone please help me & show the work for it??
Answer:
[tex]310 ^\circ F[/tex]
Step-by-step explanation:
The formula relating surface temperature in °F and time in t minutes after removal from the oven is given as
[tex]S(t)= 72 + 238 (0.97^t)\\\\\text{The initial temperature is when t = 0}\\\\\text{At t = 0}\\\\S(0) = 72 + 238(0.97^0)\\\\0,97^0 = 1 \text{ since any number raised to 0 = 1}\\\\\text{Therefore}\\S(0) = 72 + 238 \cdot 1\\= 72 + 238\\\\= 310 ^\circ F[/tex]
Using the graph determine the coordinates of the zeros of the parabola
Answer:
-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,
The area of the shaded region is 277
The length of the radius and diameter are 10.5 and 21 respectively
What is area ?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
The area of the sector = tetha/360 × πr²
= 72/360 × 3.14 × r²
= 0.628r²
area of the circle = area of the shaded part + area of sector
3.14r² = 277 + 0.628r²
3.14r²-0.628r² = 277
2.512 r² = 277
r² = 277/2.512
r² = 110.3
r = √ 110.3
r = 10.5
d = 2r
d = 10.5 × 2
= 21
therefore the radius and diameter are 10.5 and 21 respectively
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pls help me with the algebra assignment
Answer:333
Step-by-step explanation:53533535
Arthur invested $100 in an account. His account balance is shown in the table.
Arthur’s Account
Balance
Time
(years) Amount
($)
1 109.00
2 118.81
3 129.50
About how many years will it take for Arthur’s investment to double?
Responses
A.7.73 years
B.7.79 years
C.7.87 years
D.8.04 years
Answer:
Step-by-step explanation:
We can use the rule of 72 to estimate the time it takes for Arthur's investment to double. The rule of 72 states that the time it takes for an investment to double is approximately 72 divided by the annual rate of return.
To apply this rule, we need to calculate the annual rate of return that Arthur is earning on his investment. We can do this by calculating the percentage increase in his account balance from year to year.
From year 1 to year 2, his account balance increased by (118.81 - 109)/109 = 9.81/109 = 0.09 = 9%.
From year 2 to year 3, his account balance increased by (129.5 - 118.81)/118.81 = 10.69/118.81 = 0.09 = 9%.
So the average annual rate of return over this period is approximately 9%. Using the rule of 72, we can estimate that it will take approximately 72/9 = 8 years for Arthur's investment to double.
Therefore, the closest option among the given responses is option D. It will take about 8.04 years for Arthur's investment to double.
What are the measures of all angles of a isosceles triangle.
Answer:
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
Step-by-step explanation:
Solve 9x^2-6x+1=2 using the square root property. Round to the nearest hundredth if necessary.
[tex]9x^2-6x+1=2 \iff (3x)^2-2(3x)+1=2\\[/tex]
[tex](3x - 1)^2 = 2[/tex]
[tex]3x-1=-\sqrt{2} \iff 3x = 1 - \sqrt{2} \implies x_{1} = \dfrac{1-\sqrt{2} }{3}\\[/tex]
[tex]3x-1=\sqrt{2} \iff 3x = 1 + \sqrt{2} \implies x_{2} = \dfrac{1+\sqrt{2} }{3}\\[/tex]
[tex](-0.14, \ 0.8)[/tex]
What is the period of the graph of y = 5 sin (4pi x) + 3?
A. 4pi
B. 1/2
C. 3
D. 5
Answer:
Step-by-step explanation:
Equate whats inside (arguments) \sin with base period of sine function 2\pi and solve for x to get period,
\pi x=2\pi\implies x=2
So the period of the graph of the given function is precisely 2.
Hope this helps :)
(4a^-2)^-1/2 simplify
Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.
So,
(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a
Therefore, (4a^-2)^-1/2 simplifies to 4a.
Step-by-step explanation:
Levi wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Levi has 400 feet of fencing, what dimensions would maximize the area of the pen? (a) Let w be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of w
Answer:
Step-by-step explanation:
Let's call the length of the pen perpendicular to the barn "w", and the length parallel to the barn "l".
The total amount of fencing available is 400 feet. The side against the barn will be of length l, and the other two sides will each be of length w. Therefore, the total length of fencing required is:
l + 2w
This length of fencing must equal 400 feet:
l + 2w = 400
We want to maximize the area of the pen. The area of a rectangle is given by:
A = lw
We can use the equation l + 2w = 400 to solve for l:
l = 400 - 2w
Substituting this expression for l into the equation for the area, we get:
A = w(400 - 2w)
Simplifying:
A = 400w - 2w^2
So the equation to model the area of the pen in terms of w is:
A = 400w - 2w^2
What is the value of x in the figure?
63°
56°
(x-3)
The value of x in the figure and given in the task content is; x = 64.
What is the value of variable x in the given figure?As evident in the task content; the figure is a triangle with angle measures; 63°, 56° and (x - 3)°.
Since the sum of interior angles of a triangle is; 180°.
Therefore, we have;
63° + 56° + (x - 3 )= 180°
open parenthesis
63 + 56 + x - 3 = 180°
x = 180 + 3 - 63 - 56
x = 64°.
Ultimately, the value of variable, x from the triangle is; 64°.
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help please
John's family cell phone bill is $143. the family plan cost $68 plus $15 for each person on the plan.
John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
Let the number of people on John's family plan be represented by p.
According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:
C = $68 + $15p
We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:
$143 = C + A
where A represents any additional charges.
Substituting C into this equation, we get:
$143 = ($68 + $15p) + A
Simplifying, we can write:
$75 = $15p + A
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