The probability that the sample mean falls between 4800 psi and 5200 psi is 0. 0.9973.
Probability refers to the numerical descriptions of how likely an event is to occur. For the given information, the mean µ = 5000 psi and standard deviation σ = 400 psi.
For a random sample, n = 36, in order to determine the probability that the sample mean falls between 4800 psi and 5200 psi, the z test statistics for the range must be calculated.
z = (x - µ)/ (σ/√n) = (4800 - 5000)/ (400/√36) = -3
z = (x - µ)/ (σ/√n) = (5200 - 5000)/ (400/√36) = 3
Hence, the probability that the sample mean falls between 4800 psi and 5200 psi would be p ( -3< z < 3).
From the table,
p ( -2.4 < z < 2.4) = 0.9973
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Write an equation in standar form for the line that passes through (5,0) and (0,6)
The an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
We need to write an equation in standard form for the line that passes through (5,0) and (0,6)
The formula for equation of line with two points is
y - y₁ = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)
y - 0 = ((6 - 0)/(0 - 5))(x - 5)
y = 6/-5 (x - 5)
-5y = 6(x - 5)
-5y = 6x - 30
5y + 6x - 30 = 0
Therefore, the an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
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Which point is on the graph of the equation y = -3x + 4?
(-3, 4)
(2, 2)
(1, 1)
(0, -4)
Answer:
(1,1)
Step-by-step explanation:
we fill in the equation for these points to see if they are on the line
(-3,4)
4=-3(-3)+4
4=-9+4
4=-5
Not on line
2=-3(2)+4
2=-6+4
2=-2
Not on line
1=-3(1)+4
1=-3+4
1=1
On the line
-4=-3(0)+4
-4=4
Not on line
Hopes this helps please mark brainliest
Rewrite the equation in terms of x.
y =4/7(x-13)
Answer:
y=(47)xy=(47)x
Rewrite the equation as 47x=y47x=y.47x=y47x=y
Multiply both sides of the equation by 7474.74(47x)=74y74(47x)=74ySimplify both sides of the equation.Tap for more steps...x=7y4
Step-by-step explanation:
confusing bro
Answer:
x = (4/7y) + 13
Step-by-step explanation:
y = 4/7( x -13)
cross multiply
y x 7( x -3) = 4
(x - 3) = 4/7y
x = (4/7y) + 13
graph the function y=-2x-2
The graph of the function denotes a straight line which passes through the points (-1 , 0) and (0 , -2) .
The graph of the function denoted as y = -2x - 2 is in the form of a straight line as it can be written as y = mx + c the slope is -2 and y intercept is at (0,-2).
The graph of the line passes through :
At x=0 , y = -2
At x = -1 , y = 0
At x = 2 , y = -6
The line passes through (0,-2) , (-1,0) and (2,-6) .
A straight line is a line with no curves and an infinite length. Any two locations can also be connected by a straight line, but its endpoints must extend into the infinite.
A straight line results from connecting two points A (x1, y1) and B (x2, y2) along the shortest path possible and stretching the endpoints of the line to infinity.
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Enter <,> or = to make the statement true.
.320 ? .051
0.320 > 0.051
Round it up. 4 and below doesn't round and 5 and above will.
0.320. 0.051
0.320. 0.05
Look at it as 0.32 and 0.05
these would come down to 32% or 5%
as the 3 is in the tenths and the 5 is in the hundredths.
making the 3 in the tenths larger.
Simple as 30 and 5
An investor invested a total of $2900 in two mutual funds.One fund earned a 6% profit while the other earned a 4% profit.If the investors total profit was $138, how much was invested in each mutual fund?
The answer will be $1100 invested in each year.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
We'll figure out how to solve the two-equation linear system:
We'll set x equal to 8% of the investment and y equal to 5% of the investment.
Equation 1: x + y = 2900 (total invested money)
Equation 2: 0.06x + 0.04y = 138 (total interest of both investments)
25*(0.06x+0.04y = 138)
Equation 3: 1.5x + y = 3450
Eq3-Eq1
0.5x = 550
x = 550/0.5 = 1100
Hence the investment in each year will be $1100.
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2. Four out of nine dogs weigh less
than 20 pounds. What is the decimal
equivalent for the number of dogs
weighing under 20 pounds?
Repeating 0.2
0.24
Repeating 0.4
0.49
The decimal equivalent for the number of dogs weighing under 20 pounds is repeating 0.4.
Given that four out of nine dogs weigh less than 20 pounds.
We want to find the decimal equivalent for the number of dogs weighing under 20 pounds.
The total number of dogs is 9.
Number of dogs whose weight less than 20 pound is 4.
The decimal equivalent of dogs whose weight is less than 20 pound is 4/9 or 0.444
Hence, the decimal equivalent for the number of dogs weighing under 20 pounds when four out of nine dogs weigh less than 20 pounds is Repeating 0.4.
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PLEASE HELP DUE IN 2 MINUTES I NEED UNGROUNDED
Answer: wheres the question
Step-by-step explanation:
the divide fractions ? the first fraction by the ? of the second
To divide two fractions, _multiply_ the first fraction by the _Reciprocal_ of the second fraction.
What is Fraction?
A fraction represents a portion of a whole. This whole may refer to a place or a group of places. The Latin word "fractio," which means "to break," is the source of the English word "fraction." The division of food and supplies as well as the lack of a bullion currency were among the mathematical issues that the Egyptians used fractions to solve because they were the first civilization to study fractions.
Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions were first written in India with one number above the other, but without a line. The line used to divide the numerator and the denominator was only added by Arabs.
To divide two fractions, ______ the first fraction by the _______ of the second fraction.
The answer to the blanks are Multiply and Reciprocal respectively
Example:
1/2 ÷ 3/4
= 1/2 × 4/3
= 4/6
= 2/3
Hence, the answer to blanks are Multiply and Reciprocal respectively
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For each ordered pair (x, y), determine whether it is a solution to the inequality 2x+6y≤ - 12
The correct answer among the choices is letter d. From the following choices of ordered pair, (1, 0) is the set solution of the inequality 2x + 6y ≤ 10. Substituting the given pair order make the inequality a true statement. To counter check answer, substituting the pair order and solving the linear inequality will result a value to support the correct answer.
a. ( 3,1 ) (x ,y)
Substitution
2x + 6y ≤ 10
2(3) + 6(1) ≤ 10
6 + 6 ≤ 10
12 ≤ 10 ( The inequality is False)
This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.
b. (2, 2) (x ,y)
Substitution
2x + 6y ≤ 10
2(2) + 6(2) ≤ 10
4 + 12 ≤ 10
16 ≤ 10 ( The inequality is False)
This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.
c. (1, 2) (x ,y)
Substitution
2x + 6y ≤ 10
2(1) + 6(2) ≤ 10
2 + 12 ≤ 10
14 ≤ 10 ( The inequality is False)
This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.
d. (1, 0) (x ,y)
Substitution
2x + 6y ≤ 10
2(1) + 6(0) ≤ 10
2 + 0 ≤ 10
2 ≤ 10 ( The inequality is True)
The statement states that 2 is lesser than or equal to 10.
Hence we get the required answer.
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Your question was incomplete. Please find the missing content below.
Which of the following ordered pairs is a solution of the inequality 2x + 6y ≤ 10?a. (3, 1) b. (2, 2) c. (1, 2) d. (1, 0)
The following is a list of grades that students received on a recent math exam:
77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.
The teacher wants to list all test scores. Which of the following displays would represent the data in this way?
Box plot
Circle graph
Histogram
Stem-and-leaf plot
Histogram is the displays would represent the given data. Therefore, option C is the correct answer.
What is range?The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number.
Given that, the data is 77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.
The ascending order of given numbers is 62, 63, 65, 66, 75, 76, 77, 78, 78, 78, 80, 81, 81, 88, 89, 89, 91, 91, 91, 91, 92, 93, 93, 93, 95, 96.
Use the class intervals 60-70, 70-80, 80-90, 90-100, to plot the histogram for the given data set.
Hence, Histogram is the displays would represent the given data. Therefore, option C is the correct answer.
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For mutually events r1,r2 and r3, we have p(r1)=0.05
For mutually exclusive events R₁,R₂ and R₃, the value of P(R₁Q) is 3/55.
Define mutual exclusive events.Two events are said to be mutually exclusive in probability theory if they cannot happen simultaneously or at the same time. In other terms, occurrences that are mutually exclusive are referred to as discontinuous events. If two occurrences are regarded as separate ones, there is no chance that they will happen at the same moment. Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
Given,
Events:
P(R₁) = 0.05 P(R₂) = 0.6
For P(R₁ /Q)
P(R₁Q)
mutually exclusive event:
P(Q/R₁)P(R₁)/P(Q/R₁)P(Q₁) + P(Q/R₂)P(R₂) + P(Q/R₃)P(R₃)
(0.6)(0.05)/0.6(0.05) +0.4(0.6) + 0.8(0.35)
0.03/0.03 + 0.77 + 0.28
0.03/0.55
3/55
For mutually exclusive events R₁,R₂ and R₃, the value of P(R₁Q) is 3/55.
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I need helpp!
You need to Find m < B
Answer:
mAngleB = 67°
Step-by-step explanation:
The angle marked 15x is made by extending one side of the triangle. That is an exterior angle (like, its outside the triangle)
There are two angles inside the triangle that are away from that exterior angle. They are called remote interior angles. They are marked 83° and 6x+7 in this question.
Here's the rule:
If you add up the two remote interior angles it equals the exterior angle.
83° + 6x + 7 = 15x
Subtract 6x.
83 + 7 = 9x
Simplify.
90 = 9x
Divide by 9.
10 = x
Use this to find mAngleB
mAngle B = 6x + 7
= 6(10) + 7
= 60 + 7
= 67
mAngleB = 67°
Joey built a model sailboat that is similar to his real sailboat. The triangular sail on his real boat has a base of 30 feet. If the height of the sail on his model boat is 1 foot and the base is 1.25 feet, what is the height of the sail on his real boat?
Answer:
24 feet
Step-by-step explanation:
30 : 1.25 = x : 1
x = 30 / 1.25
x = 24
the pressure (p) at the bottom of a swimming pool varies directly as the depth (d) of the water. If the pressure is 125 pascal when the water is 2meters deep, find the pressure when it is 4.5 deep
Step-by-step explanation:
p varies directly with d.
that means there is a constant k, so that
p = kd
to find k we use the one set of numbers we know about
125 = k×2
k = 125/2 = 62.5
now, when the water is 4.5 meters deep :
p = 62.5 × 4.5 = 281.25 pascal
a parabola has a vertex of (2 -5) and opens down. Write the vertex equation of the parabola
The vertex form equation of the parabola whose vertex is; (2, -5) as required in the task content is; y = -(x - 2) - 5.
What is the vertex form equation of the parabola whose vertex is; (2, -5)?It follows from the task content that the vertex form equation of the parabola described in the task content is to be determined.
Since the vertex form equation of a parabola takes the form;
y = a (x - h)² + k
where the graph opens upward when a > 0 and opens downward when a < 0.
Therefore, the required vertex form equation of the parabola is; y = -(x - 2) - 5.
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A store sells a certain digital camera model for $108. During a special promotion, the camera is discounted by 40 percent. What is the discounted price?( please detailed)
Answer:
$32.4
Step-by-step explanation:
Solve the equation please help!!!!
he simplest form of quadratic equation 6y² + 5y - 4 is y = 0.5 or y = −1.33333 or in fraction y = 6 / 12 or y = −16/12.
How to solve a quadratic equation using the Quadratic Formula.
Write the quadratic equation in standard form, ax² + bx + c = 0. Identify the values of a, b, c.Write the Quadratic Formula. Then substitute in the values of a, b, c.Simplify.Check the solutions.6y² + 5y - 4
using the Quadratic Formula where a = 6, b = 5, and c = -4
y =−b±(√b2−4ac) / (√2a)
y =−5±(√5²−4(6)(−4)) / √(2(6))
y =−5±(√25−(−96)) / √12
y =−5± (√121 / √12
The discriminant b²−4ac>0. So, there are two real roots.
Simplify the radical:
y = (-5 ± 11) /12
y = 6/12 y =16/12
which becomes
y = 0.5
y = −1.33333
Hence, the simplest form of quadratic equation 6y² + 5y - 4 is y = 0.5 or y = −1.33333.
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write the expression as the logarithm of a single number or expression. assume that all variables represent positive numbers. 5log x 2logy-6logz
The expression as the logarithm of a single number or expression is log( x⁵.y/z⁶).
Define the term logarithm?A logarithm is a multiplication-based mathematics notion.
The exponent that will result in a particular value is a logarithm.
An exponent or power with which a base must be increased in order to produce a particular number.
If bˣ = n, then x is the logarithm of n here to base b, which is expressed mathematically as x = logb n. For instance, 2³ = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log₂ 8.
For the stated question;
= 5log x + 2logy - 6logz
Using the addition, division and power property.
log(m x n) = log m + log n
log(m/n) = log m - log n
= log x⁵ + logy² - logz⁶
= log( x⁵ ₓ y²) - logz⁶
= log( x⁵.y/z⁶)
Thus, the expression as the logarithm of a single number or expression is log( x⁵.y/z⁶).
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Si hace 10 años las edades de Ana y su madre eran 15 y 40, respectivamente, ¿cuál es la razón entre las edades actuales de ambas?
Opciones:
1/2
5/30
3/8
15/40
Answer:
3:8
Step-by-step explanation:
15:40
Work out the same by simplifying which they both go in 5
then doing that you can get 3/8 Or 3:8.
Hope it helps!
Spanish:
Resuelve lo mismo simplificando lo que ambos van en 5
luego haciendo eso puedes obtener 3/8 o 3: 8.
What is the sum of 1 triangle?.
The sum of the triangle angles is 180°.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The sum of the triangle angles is 180°.
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Scientists found an animal skull during an excavation and tested the amount of carbon-14 left in it. They found that 55 percent of the carbon-14 in the skull remained. How many years ago was the animal buried? round your answer to nearest whole number. (hint: a = a0e-0. 000124t. ).
Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.
55% of the Carbon is left in the skull.
If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀ which equals 0.55A₀
Using the given equation:
[tex]A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\[/tex]
[tex]t = \frac{In(0.55)}{-0.000124} \\\\t = 4821[/tex]
Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.
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Consider the rational equaton [tex]\frac{5}{x-6}\ \textgreater \ \frac{3}{x+2}[/tex]. Determine if each statement is true or false. Explain your answer.
a. [tex]-2 6[/tex] is a solution to the rational inequality.
b. The excluded values of the rational inequality are [tex]x=6[/tex] and [tex]x=-2[/tex] only
a. -26 is a solution to the rational inequality false
b. The excluded values of the rational inequality are and only - true
How to determine the solution of the inequalityInformation given in the question
5 / (x - 6) > 3 / (x + 2)
a. The inequality is solved by
5(x + 2) > 3 (x - 6)
5x + 10 > 3x - 18
collecting like terms
5x - 3x > -18 - 10
2x > -28
x > -14
Hence -26 is less than -14 so it is wrong as the solution says greater than -14
b. at x = 6
5 / (x - 6) = 5 / 0 which is infinity
at x = -2
3 / (x + 2) = 3 / 0 which is infinity
These two values are the excluded values
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Steven read a total of 21 books over 7 months. After belonging to the book club for 12 months, how many books will Steven have read in all? Solve using unit rates.
Answer:
36 books
Step-by-step explanation:
21 books / 7 months = 3 books per month
3 books per month × 12 months =
36 books
The line passes through the points (7, -2) and (-5, 7).
Write an equation for the line in standard form.
Answer:
Step-by-step explanation:
use the y=mx+b^2 formula
The function f(x) is a cubic function and a limited table of values is provided below.
Write the equation of the cubic polynomial in standard form.
The formula for a cubic polynomial function is f(x)=ax³++bx²+cx+d, where a not equal to 0.
f(x) = x³+2x²-16x-32
What is cubic function?The formula for a cubic function is f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are all real values and a 0.
A cubic polynomial function has the formula f(x)=ax3++bx2+cx+d, where an is not equal to 0. A cubic polynomial always has three zeros, which could be all the same or all different. The zeros could be real or complex, depending on the function.
If x = -4, -2, or 4 then f(x) = 0
These are the roots, then.
factors include F(x) = [(x+4)(x-4)] = (x+4)(x+2)(x+4) For example, (x+2) f(x) = (x2-16) (x+2) f(x) = x3+2x2-16x-32
A cubic equation might have three real roots, similar to how a quadratic equation could have two. However, a cubic equation always has at least one real root, unlike a quadratic equation, which may not have any real solutions.
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how many 5-in.-diameter, 1/4-in.-thick disks can be fitted into a 4-ft long, 5 1/4-diameter cylindrical container?
There can be 228 disks fit into the cylindrical container
Here it is given that the diameter of the disk is 5 inches.
Therefore, the radius of the disk is 2.5 inches.
The height of the disk is 1/4 inch,
Now the cylindrical container had a height of 4 feet
1 foot = 12 inches
Hence,
4 feet = 48 inches.
Hence, the height is 48 inches.
The radius of the container is half of 5 1/4 inches
= 2.725 inches.
The number of disks that can be fit
= Volume of the container/volume of disk
The volume of any cylinder
= π X radius² X height
Hence, the volume of the disk is
π X 2.5² X 0.25 cubic inches
= 1.5625π cubic inches
= 4.909 cubic inches
The volume of the cylinder is
π X 2.725² X 48 cubic inches
= 356.43π cubic inches
= 1119.758 cubic inches
Hence the number of disks that can fit in the container
= 1119.758/4.909
= 228.103
Since the number of disks cannot be in decimal
228 disks can be fitted in.
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A sailor entered a race and made a round trip of 213.709 miles. What is 213.709 rounded to the nearest hundredth? Choose the number to complete the statement.
The estimate for the number of miles traveled is
Choose...
.
Part B
Which of the following statements explains how you should round 213.709?
A.
Since the digit in the hundreds place is less than 5, keep the digit in the hundredths place. Then drop the digits on the right.
B.
Since the digit in the hundredths place is less than 5, keep the digit in the tenths place. Then drop the digit in the hundredths and thousandths places.
C.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
D.
Since the digit in the hundredths place is less than 5, leave the digit in the hundredths place and drop all the numbers on the right.
The estimate for the number of miles traveled is, 213.71.
What rounding the decimal number?
If the following digit in the correct location is less than 5, round the number down; if it is 5 or more, round the number up. A certain level of accuracy is required when rounding decimal values.
As given, a sailor entered a race and made a round trip of 213.709 miles.
We have to round the decimal number 213.709 to nearest hundredth.
Here the digit on thousands place is greater or equal to 5.
So, we have to increase the number on hundredths place by 1, and drop the digit in the thousandths place.
Hence, the number becomes, 213.71.
Therefore, the option C is the correct.
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there are 120 people in a theatre 72 are female of these 41 purchase an ice cream 36 males purchase and ice cream use this information to compete the frequency tree
There are 120 people in a theatre. 72 are female and 48 are male. 12 females purchase an ice cream and 31 males purchase an ice cream.
What is Frequency Tree?
Frequency trees display the real frequency of certain events. They can display the same data as a two-way table, but frequency trees are more readable since they illustrate the frequency hierarchy. Probability trees depict the likelihood of a series of occurrences.
Solution:
From the question, we can see the there are 120 people in the theatre.
Since, there are 72 females in the theatre we can find the total number of males by 120-72 = 48
Also, the male who purchased Ice Cream were 36 therefore, the males who did not purchased Ice Cream are 48-36 = 12
And, the females who purchased Ice Cream are 41. So, the female who did not purchased Ice Cream are 72 - 41 = 31
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Pls explain the answer thank u
Answer:
x=2
Step-by-step explanation:
The line to be parallel and have a point at (2,-5)
here is a picture attached for better understanding
