The probability that a sample of 120 female graduates will = 0.8905
what is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
= |y -µ| ≥ 0.60
z = y -µ /σ√n
= 0.60/4.10√120
= 0.60/0.3742770
=1.60
Pr ( y -µy) ≤ 0.60 = P |z|≤1.60
=P ( -1.60≤ Z≤ -1.60)
=P (Z ≤ 1.60) -P ( Z≤ -1.60)
= 0.9452 - 0.0547 using z table
= 0.8905
Female graduates
mean = 27.83
sd = 4.10
sample = 120
µx = 27.83
σx = σ/√n
= 4.10/√120
a) P (X bar > 27.83)
= P (X bar -µx)/ σx > 27.83-27.83/4.10/√120
= P ( z > -1.60)
= 0.9452
For men
Mean=µ=37.39
Sd=σ=4.60 ,n=50
Probability that sample mean within $1.00 of the population mean
u-1=37.39-1=36.39
u+1=37.39+1=38.39
P = (36.39 <X bar < 38.39)
= P [tex]\frac{36.39-37.39 }{4.60/\sqrt{60} } < \frac{X bar - µ}{σ/\sqrt{n} } < \frac{39.39-37.39}{4.60/\sqrt{60} }[/tex]
= P ( -1.6839 < Z <1.6839
= P ( -1.68 < Z <1.68)
= P (Z < 1.68) - P(Z < -1.68)
= 0.9535- 0.0465
= 0.9070
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Hailey goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Hailey decides to leave a tip of 24% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Hailey paid.
The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .
What is business Mathematics?
Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.
According to Question:
let the the subtotal on the bill was xx dollars
A tax of 8% is added on bill then Bill becomes xx + 8% of xx
The of 8% on bill = (108/100)xx
Now the Final bill = xx + (108/100)xx
= (208/100)xx
Hailey decides to leave a tip of 24% on the entire bill (including the tax)
So the Total Amount = (208/100)xx + 24% of Final bills
⇒
24% of (208/100)xx = (208/100)(124/100)xx
The Total amount = (208/100)xx +(208/100)(124/100)xx
Let the Amount be A
hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx
⇒ A = (52/25)xx +(52/25)(31/25)xx
⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)
⇒ 625A = 1300xx + 1612xx
⇒ 625A = 2912xx
⇒ A = (2912/625)xx
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Are the two triangles congruent? If so, write the congruence statement.
△KML is congruent to △QNP (△KML ≅ △QNP) under SSA conditions.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
They are in alignment with one another when moved.
If two triangles meet all 5 requirements for congruence, then they are congruent.
They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).
So, in the given triangle:
Prove that: △KML ≅ △QNP
∠L = ∠P = 90° (Equal: Given)
ML = QP = 12 units (Equal: Given)
Mk = QN = 15 units (Equal: Given)
So, △KML ≅ △QNP is under SSA condition.
Therefore, △KML is congruent to △QNP (△KML ≅ △QNP) under SSA conditions.
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write the equation of a parabola whose vertex is (-3,4) and passes through: (2,8). Put in vertex form.
The equation of the parabola that has a vertex (-3,4) and passes through (2,8) is 25y = 4x² + 24x + 13.
What is parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the DirectX and focus, respectively.
Given:
The vertex = (-3, 4) and the point = (2, 8)
Write the equation using the standard form given below,
[tex]y = a (x - h)^2 + k[/tex]
y = a[x - (-3)]² + 4
y = a(x + 3)² + 4
Now put the coordinates,
8 = a (2 + 3)² + 4
8 = 25a + 4
a = 4 / 25
Put the value of a in the above equation,
y = 4/25 × (x + 3)² + 4
25y = 4 (x² + 9 +6x) + 100
25y = 4x² + 36 +24x + 100
25y = 4x² + 24x + 13
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4. Find the lengths of the sides of a triangle with vertices: (0, 0), (5, 0), (5, 12). (1 point)
O5, 12, 12
O5, 5, 12
O5, 12, 5
O5, 12, 13
The lengths of the sides of the triangle are 5, 12, and 13.
So the correct option is the last one.
How to find the lengths of the sides?Remember that if we have two points (x₁, y₁) and (x₂, y₂), the distance between these two points is given by the formula:
d = √( (x₁ - x₂)² + (y₁ - y₂)²)
Here we know that the vertices of our triangle are the points:
(0, 0), (5, 0), (5, 12)
And we want to find the lengths of the sides.
We can get the length of the first side using the points (0, 0), (5, 0)
d₁ = √( (0 - 5)² + (0 - 0)²) = 5
The length of the second side is: (5, 0), (5, 12).
d₂ = √( (5 - 5)² + (0 - 12)²) = 12
The length of the third is side is given by the points (5, 12) and (0, 0)
d₃ = √( (5 - 0)² + (12 - 12)²)
d₃ = √(25 + 144) = 13
Then the correct option is the last one:
5, 12, 13.
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Please help! Division of Polynomials, Find the quotient and remainder.
First:
Quotient: [tex]2x^{2} -11x+58[/tex]
Remainder: [tex]-294[/tex]
Second:
Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]
Remainder: [tex]422[/tex]
Third:
Quotient: [tex]2x-3[/tex]
Remainder: [tex]12[/tex]
In triangle XYZ , A is the midpoint of overline XY . B is the midpoint of overline YZ . and C is the midpoint of overline XZ; AC = 5 , BC = 6 , and XZ = 15 What is the perimeter of triangle XYZ ? Enter your answer in the box .
The perimeter of the triangle XYZ according to the midsegment theorem is 37
What is the midsegment theorem?The midsegment theorem states that the segment that is obtained by joining the midpoints of two sides of a triangle is parallel to the third side and it is half the length of the third side of the triangle.
The specified parameters are;
The midpoint of [tex]\overline{XY}[/tex] = A
The midpoint of [tex]\overline{YZ}[/tex] = B
The midpoint of [tex]\overline{XZ}[/tex] = C
The length of segment AC = 5
The length of segment BC = 6
The length of side XZ = 15
The segments AC, BC, and AB are midsegments of the triangle XYZ
According to the midsegment theorem, we get
AC = 0.5 × [tex]\overline{YZ}[/tex]
BC = 0.5 × [tex]\overline{XY}[/tex]
AB = 0.5 × [tex]\overline{XZ}[/tex]
Therefore;
2 × AC = [tex]\overline{YZ}[/tex]
2 × BC = [tex]\overline{XY}[/tex]
2 × AB = [tex]\overline{XZ}[/tex]
[tex]\overline{YZ}[/tex] = 2 × 5 = 10 (substitution property)
[tex]\overline{XY}[/tex] = 2 × 6 = 12 (substitution property)
The perimeter of the triangle = [tex]\overline{YZ}[/tex] + [tex]\overline{XY}[/tex] + [tex]\overline{XZ}[/tex]
Plugging in the values, of [tex]\overline{YZ}[/tex], [tex]\overline{XY}[/tex], and [tex]\overline{XZ}[/tex] we get;
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An isosceles triangular prism has a triangular
end with a base of 16 feet, an altitude of 6 feet,
and a side length of 10 feet. The height of the
prism is 18 feet. What is the surface area of the
prism?
a- 520
b- 850
c- 744
d- 635
An isosceles triangular prism, its surface area becomes: 568 feet²
What is an isosceles triangular prism?The faces of a polyhedron called an isosceles triangular prism are made up of polygons. It has six edges, five faces, and five vertices. Isosceles triangles make up the two portions at the base that face each other and rectangles make up the vertical faces of the five faces.
where the isosceles triangle's base has equal sides measured in "a" units, each triangle's base measured in "b" units, the triangle's height measured in "h" units, and the length of the congruent rectangles measured in "l" units.
The surface area of an isosceles triangular prism is:
Surface area = (b × h) + (2× l × a) + (l × b)
here, b = the base of each of the triangle = 16 feet
h = the height of the triangle = 18 feet
l = length of the congruent rectangles = 10 feet
a = isosceles triangle in the base have the equal sides be "a" units = 6 feet
Now, Surface area = (16 × 18) + (2 × 10 × 6) + (10 × 16)
or, Surface area = 568 feet²
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Juan borrowed $2000 for 1 year and
paid 15% interest. How much
interest did he pay in a year?
Answer:At the rate of 15% the amount of interest on $2000
Step-by-step explanation:
simple amount= Principle(1+rt)
where r= rate of inetrest
t= time
principal is initial amount
therefore, amount=2000(1+15*1)
Amount = $2,300.00
Interest = Amount - Principal = $300.00
Answer:
Step-by-step explanation:
Interest = Principle * Rate * Time /100
Principle = $2000
Rate = 15 %
Time = 1 year
I = 2000 * 15 * 1/100
I = 300
Juan has to pay $300 in a year
a restaurant is introducing a new gluten-free recipe for the topping in its baked zucchini recipe. the chef will continue to use this topping if less than 8% of her customers complain about the new taste. using a random sample of customers, she conducts a hypothesis test with h0: the complaint rate is 8%, and ha: the complaint rate is less than 8%. what is a type i error and its consequence in this context?
By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.
What does testing your hypotheses mean?
To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.
First, a hazy assumption about the parameter or distribution is made.
What is hypothesis testing, and how can it be used?
A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.
The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.
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A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground. Find the height to which the ladder will reach the wall.
A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.
What is height?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.
From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.
let, h = height of ladder
Given that,
length of ladder = 12 ft
angle with the ground = 52°
As we know,
sinθ = h/12
or, sin (52°) = h/12
or, 0.7880 = h/12
or, h = 9.456 foot.
the height to which the ladder will reach the wall 9.456 foot.
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(URGENT!!) In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.
Responses
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ
The equivalent ratios to tan F = EL/ EF = OS/OJ
Similar triangles:Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.
All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.
Given that
△FEL∼△JOS
That means △FEL and △JOS are similar triangles
As we know tan θ = Opposite side / Adjacent side
From the triangle △FEL,
=> tan F = EL/EF
By the given information,
The similar triangle's corresponding sides will have the same ratio
=> EL/ EF = OS/OJ
Therefore
The equivalent ratios to tan F = EL/ EF = OS/OJ
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q1.2: what power of 2 is the smallest representable positive normalized number? submit the exponent only.
The smallest representable positive number is 2149, or roughly 1.4*10-45.
Lets take a 32-bit floating point integer (IEEE 754) with the following bits,
0-22 for the mantissa (23 bits), 23-30 for the exponent ( 8 bits), and 31 for the sign (1bit)
The decimal counterpart of this expression would be if we put all zeros in the mantissa and all ones in the exponent.
The way of representing huge numbers in terms of powers is known as an exponent.
Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.
The exponent is represented by the symbol ^ . This symbol is known as a carrot . As an illustration, 4 raised to 2 can be expressed as 4^2 .
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is 1/x = 3 nonlinear?
Answer:
it is linear
Step-by-step explanation:
i took the test.
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 22 cards, which was 2% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:
22 X 50= 1100 cards because 100 dived by 2 = 50.
Step-by-step explanation:
Write "less" or "greater" in the blank.
972 is
than 792
Answer:
greater
Step-by-step explanation:
972 is a higher number than 792 so the answer is greater
Answer:
972 is greater than 792
Step-by-step explanation:
972 > 792
8. a factory makes silicon chips for use in computers. it is known that about 90% of the chips meet specifications. every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded. what is the approximate mean and standard deviation of the number of chips meeting specifications? (a) u
The approximate mean and standard deviation of the number of chips meeting specifications are: μ = 16.2; σ = 1.273
In this question, we have been given a factory makes silicon chips for use in computers. it is known that about 90% of the chips meet specifications. every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded.
we need to find the approximate mean and standard deviation of the number of chips meeting specifications
Since 90% meet specifications we can say p = 0.9
So, q = 1 - p
q = 1 - 0.9
q = 0.1
here, a sample size is n = 18
So, the mean would be,
μ = np
μ = 18 * 0.9
μ = 16.2
And the standard deviation would be,
σ = √npq
σ = √(18 * 0.9 * 0.1)
σ = 1.273
Therefore, the mean (μ) = 16.2 and the standard deviation (σ) = 1.273
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Solve the equation -3.5(x-14)+9x=5.5x + 49. Which statement is true ?
Answer:
Step-by-step explanation:
Answer:
-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.
Step-by-step explanation:
What’s the force on an object with a mass of 10 kg and an acceleration of 4 m/s
The force on the object is 40N
What is force?Force can be described as the influence that can change the motion of an object.
It is seen as an external agent having the capability of changing a body's state of motion or rest.
It causes b in velocity of an object with mass , that is, to accelerate. Force can also be described as either a push or a pull.
It is described as a vector quantity, that is, it has both magnitude and direction.
The formula for determining force is given as;
F = ma
Where;
f is the force on the objectm is the massa is the accelerationSubstitute the values
F = 10(4)
F = 40N
Hence, the value is 40N
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Miguel’s Skate Shop is having a sale on skateboards. The original price for its Extreme Skateboard is $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard?
The required percent decrease in the price of the skateboard is 40%.
What is the percentage?
A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here, we have
Original price = $84.50
sale price = $50.70
Percent decrease = 84.50-50.70/84.50 × 100 = 40%
Hence, the required percent decrease in the price of the skateboard is 40%.
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A square has sides of length 15 kilometers. What is the area?
Answer:
The area of the square is 225 square kilometres.
Step-by-step explanation:
Given;A square has sides of length 15 kilometers,Side (s) = 15 kmTo Find;Area of square.Formula;Area = (side)²So,
A = (15)² km
A = 225 km²
Thus, The area of the square is 225 square kilometres.
Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question
Answer:
10 years old
Step-by-step explanation:
Please help, I will give u 20 points and I will choose u as the brainlyest answer. ( only if you get it right)
The missing factor for A in the model is 3/4
The missing factor for B in the model is 1/5The factor pair is 3/20How to determine the missing factor for A?From the question, we have the following parameters that can be used in our computation:
Length of column A = 4
Shaded region in column A = 3
This means that
The missing factor = Shaded region/Length of column A
Substitute the known values in the above equation, so, we have the following representation
The missing factor, A = 3/4
How to determine the missing factor for B?Here, we have
Length of column B = 5
Shaded region in column B = 1
This means that
The missing factor = Shaded region/Length of column B
Substitute the known values in the above equation, so, we have the following representation
The missing factor, B = 1/5
The factor pairIn (a) and (b), we have
The missing factor, A = 3/4
The missing factor, B = 1/5
So, we have
Pair = 3/4 * 1/5
Evaluate
Pair = 3/20
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Mrs. Green sold of her cookies. She gave 36 of the remainder to her neighbour and kept 48 for her family. How many cookies did Mrs. Green sell?
Answer:
84
Step-by-step explanation:
Let's call the number of cookies Mrs. Green sold "x". We can then write the following equation to represent the information given in the problem:
x - 36 - 48 = 0
Solving for x, we get:
x = 36 + 48
Mrs. Green sold 36 + 48 = 84 cookies.
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Solve for x. Round to the nearest tenth of a degree, if necessary
!HURRY PLEASE ITS DUE IN AN HOUR!
The measure of the angle x would be 30.26°.
What are inverse trigonometric functions?
Inverse trigonometric functions are functions that "undo" the action of the trigonometric functions. They allow us to find the angles of a right triangle given the values of the sides, or to find the values of the sides given the angles.
In the given triangle, by using sine ratio we can write
sin(x°) = BC/AC
[tex]sin(x^o)=39/74\\\\x^o=sin^{-1} \frac{39}{74}\\\\x^o=sin^{-1}{0.5270}\\\\x^o=30.26^o[/tex]
Hence, the measure of the angle x would be 30.26°.
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there are 97 men and 3 women in an organization. a simple random sample of 5 people is taken to form a committee. what is the probability that the committee includes all 3 women?
The probability that the committee includes all 3 women is 0.00018
In this question, we have been given there are 97 men and 3 women in an organization.
A simple random sample of 5 people is taken to form a committee.
We need to find the probability that the committee includes all 3 women.
Total number of people in the organization: 97 + 3 = 100
Usinng combination formula the possible number of 5 people committee:
100C5
= 100! / 5!(100 - 5)!
= 75287520
The number of outcomes for the committee includes all 3 women would be:
5C3 = (97C2)*3
= 13968
So, the probability that the committee includes all 3 women would be,
P = 13968 / 75287520
P = 0.00018
Therefore, the required probability is 0.00018
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what is 22 divided by a number s
Answer:
22 divided by 2 is 11
Step-by-step explanation:
if two cities lie on different tectonic plates, and those plates are moving so that the cities are approaching each other, how many years will it take for the two cities to be situated adjacent to each other? los angeles is 630 km south of san francisco. the plate under los angeles is moving north about 36 mm per year relative to the plate under san francisco. given this average rate of plate movement, how long will it take for los angeles to be located next to san francisco? show your work.
It will take about 18 million years for Los Angles to be located next to san Francisco.
The distance traveled is 630km (380 miles), and the net distance moves is 36mm per year.
We can use this formula to determine the answer :
Time = distance/rate
630 km = 630,000 m = 630, 000,000 mm
Time = 630,000,000 mm/ 36mm/year = 17,500,000 year
We could also put these dimensional relationship together as follows and then cancel units that occur in both the numerator and the denominator .
We are left with an answer in number of years:
630 km × [tex]\frac{1000m}{1km 1m}[/tex] × [tex]\frac{1000mm 1 year}{36mm}[/tex] = 17,500,000 year
Hence, It will take about 18 million years for Los Angles to be located next to san Francisco.
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Solve for x
O4
O5
O-10
O12
Answer:
x = 5
Step-by-step explanation:
Firstly, we know that corresponding angles are the same. So we can say that 25x + 5 = 26x
Let’s simplify this equation:
25x + 5 =26x
-25x -25x
5 = x
Therefore, x = 5.
2/5 divided by 3/8 as a fraction
Please I need some help quickly, thank you <3
A triangle has vertices (0,0), (2,4), and (5,1). What are the coordinates of the circumcenter?, or the same triangle with vertices (0,0), (2,4), and (5,1), what are the coordinates of the orthocenter?
Answer:
[tex]Circumcenter =(2,333, 1.3333) \;or\; \left(2\dfrac{1}{3}, 1\dfrac{1}{3}\right)[/tex]
[tex]Orthocenter = (2.3333, 2.3333) \;or\;\left(2\dfrac{1}{3},2\dfrac{1}{3}\right)[/tex]
Step-by-step explanation:
