When is a standard normal random variable, the probability of P(–1.20 ≤ z ≤ 1.50) is 0.8181.
What is the probability?The probability illustrates the likelihood of events.
From the information, it's important to note that P(–1.20 ≤ z ≤ 1.50) will be:
= P(Z ≤ 1.50) - P(Z ≤ -1.20)
= P(Z ≤ 1.50) - [1 - P(Z ≤ -1.20)]
It should be noted that by using the normal z table, the probability of the corresponding z score will be 0.9332 and 0.8849.
This will be:
= 0.9332 - (1 - 0.8849)
= 0.8181
Therefore, the probability is 0.8181.
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(x-2x³-29x² - 43x+8)÷(x-7)
Answer:
-2x^2 - 43x - 343 - 2393/x-7
v+8w=4v,for v
-m+5n=-2, for n
Answer:
v = 8w/3,n = (m - 2)/5.---------------------------
Given equationsv + 8w = 4v and - m + 5n = - 2Solve the first equation for vv + 8w = 4v4v - v = 8w3v = 8wv = 8w/3Solve the second equation for n- m + 5n = - 25n = m - 2n = (m - 2)/5Answer:
Value of v = (8w)/3Value of n = (m - 2)/5Step-by-step explanation:
1) v + 8w = 4v, for v?
→ v + 8w = 4v
→ 8w = 4v - v
→ 8w = 3v
→ [ v = (8w)/3 ]
Thus, value is (8w)/3.
2) -m + 5n = -2, for n?
→ -m + 5n = -2
→ 5n = -2 + m
→ 5n = m - 2
→ [ n = (m - 2)/5 ]
Thus, value is (m - 2)/5.
Can you help me solve this problem?
The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:
0.1131 = 11.31%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion and the sample size are given as follows:
p = 0.73, n = 80.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.73[/tex].[tex]s = \sqrt{\frac{0.73(0.27)}{80}} = 0.0496[/tex]The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (0.67 - 0.73)/0.0496
Z = -1.21
Z = -1.21 has a p-value of 0.1131.
Hence the probability is:
0.1131 = 11.31%.
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Assessment Practice
5. A science teacher has $225 to spend on lab equipment.
He buys 4 posters with a guide to classifying rocks, for
$19 each. Student rock collections cost $9 each. How
many rock collections can he buy? Explain how you solve.
Use one or more equations and bar diagrams in your
explanation. Tell what your variables represent. 4.AR.1.1.4.AR.2.2
Answer:
Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve
Let
x -----> number of rock collections that he can buy
so
the algebraic expression that represents this situation is
Solve the inequality for x
subtract 76 both sides
Divide both sides by 9
therefore
The maximum number of rock collections that he can buy is 16
Step-by-step explanation:
The equation is 9x+76=225 and the number of rock collections he can buy is 17.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a science teacher has $225 to spend on lab equipment.
Let the number of rocks collected be x.
He buys 4 posters with a guide to classifying rocks, for $19 each.
That is 19×4=76
Student rock collections cost $9 each.
Now, 9×x=9x
So, the equation is 9x+76=225
Subtract 76 on both the sides of equation, we get
9x=149
Divide 9 on both the sides of equation, we get
x=16.5
x≈17
Therefore, the number of rock collections he can buy is 17.
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FIRST ANSWER GETS FIVE STARS AND BRAINLIEST!
Pine Street, Rector Street, and Taylor Street intersect to form a triangular-shaped park as shown.
(picture below)
What is the correct order of the lengths of the streets from longest to shortest?
Answer:
Rector, Pine, Taylor
Step-by-step explanation:
The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!
i need some help on these, can anybody help me?
Which algebraic expression represents the amsplit the cost of a $20.00 gift?
A. f + 20
B. 20f
C. 20 ÷ f
D. f ÷ 20
Answer:
The answer is C: 20 ÷ f
Step-by-step explanation:
What is the solution to the equation 1/3x + 2/9x =10
The solution to x in the equation is 1/3x + 2/9x =10 is 18
To solve for x we follow the step;
Step 1: Combine the equation multiple into single fraction
1/3x + 2/9x =10
[tex]\frac{x}{3}[/tex] +[tex]\frac{2x}{9}[/tex] =10
Step 2: Find the common denominator
[tex]\frac{3x}{9}[/tex] + [tex]\frac{2x}{9}[/tex] =10
Step 3: Add the fraction with common denominator
[tex]\frac{3x +2x}{9}[/tex]= 10
[tex]\frac{5x}{9}[/tex] =10
Step 4: Cross multiply
5x = 9(10)
5x = 90
Step 4: Divide both 5
[tex]\frac{5x}{5}[/tex] =[tex]\frac{90}{5}[/tex]
x= 18
Therefore, the solution for x in the equation is 18
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work out the size of angle x 24
Answer:
78°
Step-by-step explanation:
You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.
Base angleThe two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...
24° +2x = 180°
12° +x = 90° . . . . . . divide by 2
x = 78° . . . . . . . subtract 12°
The measure of angle x is 78°.
Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
Given,
The share bought by Kyle of company XYZ = $50,000
The share price = $100
The share price after an year = $110
We have to find the gain amount by Kyle when Kyle sells all his shares.
Here,
We can apply Unitary method;
100 ⇒ 110
50000 ⇒ x
Compute;
100x = 110 x 50000
x = (110 x 50000) / 100
x = 110 x 500
x = $55000
Now,
Kyle gains,
55000 - 50000 = $5000
That is,
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
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find zeros f(x)=x^4-6x^3-21x^2=150x-100 given k=5
The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100 are 0.6511 and 8.262 respectively
Zeros of a PolynomialZeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.
The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.
To find the zeros of this polynomial function, we have to write the function appropriately.
x⁴ - 6x³ - 21x² = 150x - 100
x⁴ - 6x³ - 21x² - 150x - 100 = 0
The roots of this function is 0.6511 and 8.262 respectively
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1. Given segment AB with A(-3, 2) and B (5, -4). If point P lies on segment AB such that the ratio of
AP to PB is 2:6. Find the coordinates of p
The coordinates of P is ( -1 , 0.5) .
What is section formula ?
We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.
Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio of m:n then,
=> (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]
Here A[tex](x_1,y_1)[/tex] =( -3,2) and B[tex](x_2,y_2)[/tex] = (5,-4) and m:n = 2:6
Then,
=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]
=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]
=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]
=> (x,y) = (-1,0.5)
Hence the coordinates of P is (-1 , 0.5) .
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A plant manufactures part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeters.
Question:
If one part is randomly selected, find the probability that the part is between 10.8 and 12.8 centimeters.
The probability that the plant manufactures a part between 10.8 and 12.8 centimeters 13%
How to find the probability that the part is between 10.8 and 12.8 centimetersThe probability is solved z scores, this measures the amount of standard deviation sample X is from mean. the formula is below
z = (X - μ) / σ
Definition of variables
mean, μ = 16.3 centimeters
standard deviation, σ = 2.5 centimeters
X = 10.8 and 12.8 centimeters
z score, z
substituting into the formula
for X = 12.8 centimeters
= (X - μ) / σ
= (12.8 - 16.3) / 2.5
= -1.4
the p value for z of -1.4 = 0.161513
for X = 10.8 centimeters
= (X - μ) / σ
= (10.8 - 16.3) / 2.5
= -2.2
the p value for z of -2.2 = 0.027807
the probability is calculated as below
0.161513 - 0.027807= 0.133706
= 0.13
=13%
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The formula for finding the surface area of a cube is 6s2, where s is the length of each side of the square. Evaluate for s=10 to find the number of square centimeters (cm2) for the surface area of a cube with a side length of 10 cm. i need helpp
The surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
Given:
The formula for finding the surface area of a cube is 6s2.
side length s = 10 cm.
Surface area of a cube = 6[tex]s^{2}[/tex] = 6*s*s
= 6 * 10 * 10
= 60 * 10
= 600 [tex]cm^{2}[/tex].
Therefore the surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
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Does anyone know the answer to this problem?
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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Juan is playing a game in which he can win $100 with probability 0.2, $300 with probability 0.3, and $500 with probability 0.5. What is the expected value of Juan's winnings?
Juan's winnings has an expected value of $360
How to determine the expected value of Juan's winnings?The given parameters in the question are:
$100 with probability 0.2,
$300 with probability 0.3,
$500 with probability 0.5.
The expected value is then calculated as
E(x) = Sum of (amount * probability)
Substitute the known values in the above equation, so, we have the following representation
E(x) = 100 * 0.2 + 300 * 0.3 + 500 * 0.5
Evaluate
E(x) = 360
Hence, the expected value is $360
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PLEASE HURRY I WANT TO FIISH MY TEST PLEASE ASAP!!!
Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.
The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 32. This will be illustrated thus:
1/4(32 - 4) ≤ 1/8 (32 - 16)
= 1/4(28) ≤ 1/8(16)
= 7 ≤ 2
In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.
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hole me out on this thanks
Answer: [tex]5^{2} + 4[/tex]
Step-by-step explanation:
[tex]2 + 3^3[/tex] =?
2 + 27 = 29
10 * 2 - 9 = 20 - 9 = 11
[tex]5^2 + 4[/tex] = 25 + 4 = 29
[tex]5^3\\[/tex] = 5 * 5*5 = 125
3+ 4 * 3 = 3 + 12 = 15
The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
When a person from this group is selected at random, the probability that this person has type AB blood is 3/40
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:
= Number of AB blood type / Total number of people
= 15 / 200
= 3/40
The probability is 3/40.
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There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?
Answer:
1/5
Step-by-step explanation:
equation: 3/5-2/5=x
we can multiply the whole equation by 5 so that we can easily subtract the numbers
3-2=1
now we divide it by 5 so that we get our number in a fraction
after we divide we get 1/5
A plant manufactures parts whose links are normally distributed with a mean of 16.3 cm and a standard deviation of 2.5 cm if one part is randomly selected find the probability that the part is between 10.8 and 12.8 cm
The probability that the part is between 10.8 and 12.8 cm is 0.0669.
What is a normal distribution?
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.
Here, we have
Mean = 16.3cm
Standard deviation = 2.5cm
We have to find the probability that the part is between 10.8 and 12.8 cm
Now,
we know that z = (x−μ)/σ
putting values in the normal distribution formula, we get
P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)
= P ( -2.2 < z < -1.4)
P( 10.8 < x < 12.8) = 0.0669, by normal distribution table
Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.
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Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
The amount that Katy would have saved in her savings account in 2 years is $16, 000
How to find the amount saved?Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time
Principal = $100, 000
Interest rate = 8%
Time = 2 years
The amount that Katy would have saved is:
= Principal x Interest Rate x Time
= 100, 000 x 8% x 2
= $16, 000
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The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?
A total of 12 5/8 pages is not meant for advertisement
How to determine the number of pages that are not for adverts?From the question, we have the following parameters
First section = 16 pages
Pages for advertisement = 3 and 3/8 pages
Rewrite the above parameters as
First section = 16 pages
Pages for advertisement = 3 3/8 pages
The number of pages that are not for adverts is then calculated as
Pages not for adverts = First section - Pages for advertisement
Substitute the known values in the above equation
So, we have the following equation
Pages not for adverts = 16 - 3 3/8
Evaluate the difference
Pages not for adverts = 12 5/8
Hence, the number of pages that are not for adverts is 12 5/8 pages
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Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values
Explain about the absolute values?Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.
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The sum of two odd consecutive integers is 88. Find the integers.
Answer:
43, 45 are the numbers
Step-by-step explanation:
Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
Marvin is helping his teachers plan a field trip. There are 136 people going on the field trip and each school bus holds 51 people. What is the minimum number of school buses they will need to reserve for the trip?
Answer: 3 busses
Step-by-step explanation:
Given the inequality 4x ≤ 28, determine the value of x.
Step-by-step explanation:
Given the inequality 4x ≤ 28, determine the value of x.
4x ≤ 28
divide both sides by 4:
4x/4 ≤ 28/4
x ≤ 7
set builder notation: (-∞, 7]
answer:
The value of x is 7.
Step-by-step explanation:
4x ≤ 28 | divide both sides by 4
4x / 4 = x and 28 / 4 = 7
therefore, x ≤ 7
student enrollment at a local school is concerning because the number of student has dropped to 504, which is 20% decrease from the previous year. what was the student enrollment the previous year?
The student enrollment the previous year is 630 students.
How to calculate the number of students?Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x
Based on the information given, this will be illustrated as:
x - (20% × x) = 504
x - 0.2x = 504
0.8x = 504.
Divide.
x = 504 / 0.8
x = 630
There were 630 students.
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3.) Johannes sold an order of 3 Strawberry pies
for $12.50 each. She paid her assistant
$1.10 for each Strawberrye pie sold. How much
money did Johannesearn from the pies sold?
Answer:
$34.20
Step-by-step explanation:
Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.
We know that there were 3 pies sold so you must solve the equation below
11.40*3
The answer is $34.20
