The probability that a random sample of 50 seniors has a mean score of at most 415 is given as follows:
0.1894 = 18.94%.
How to obtain probabilities using the normal distribution?The 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 obtained 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 obtained 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, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 425, \sigma = 80, n = 50, s = \frac{80}{\sqrt{50}} = 11.31[/tex]
The probability that they scored at most 415 is the p-value of Z when X = 415, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (415 - 425)/11.31
Z = -0.88
Z = -0.88 has a p-value of 0.1894.
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3. A gallon of paint covers about 500 square feet. How many square feet will 1 4/5 gallons
of paint cover?
A 650 ft²
C 800 ft²
B 750 ft2
D 900 ft²
Answer:
To solve the problem, we simply need to multiply 1 4/5 (or 9/5) by 500:
1 4/5 gallons x 500 ft²/gallon = 9/5 gallons x 500 ft²/gallon = 4500/5 ft² = 900 ft²
Therefore, 1 4/5 gallons of paint will cover 900 square feet. The answer is D.
Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). Mark this and return
The variable y is directly proportional to x, which is the definition of direct variation.
What is coordinate geometry?The intersection of two perpendicular lines, the x-axis and the y-axis, results in a 2D plane known as a coordinate plane. In geometry, a coordinate system is a method for calculating the positions of the points using one or more integers or coordinates.
The graph that represents a function with direct variation is a coordinate plane with a line passing through (0, 0) and some other point that is not the origin.
Out of the given options, the graph that represents a function with direct variation is the coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).
This is because the equation of this line can be written in the form y = mx, where m is the slope of the line. In this case, the slope is:
m = (0 - (-2)) / (-4 - 0) = 1/2
So the equation of the line is y = (1/2)x - 2, which is in the form of y = kx, where k = 1/2. This means that y is directly proportional to x, which is the definition of direct variation.
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is the square root of 2,809.
Answer:53
Step-by-step explanation:
Complete the inequality for this graph.
y <?
The inequality for this graph is given as follows:
y < 2.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.< x: amount less than x. -> to the left of x with an open dot at the number line. -> below the dashed horizontal line y = x on the coordinate plane.≥ x: amount at least x. -> to the right of x with a closed dot at the number line. -> above the solid horizontal line y = x on the coordinate plane.≤ amount at most x. -> to the left of x with a closed dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.For the graph in this problem, the inequality is composed by the values that are below y = 2, with an open interval as the line is dashed and not solid, hence it is defined as follows:
y < 2.
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7 years ago, Elijah won some money in the lottery and put it in a
bank account that earns 12% interest compounded annually. If
Elijah currently has $800.00 in the bank account, how much
interest has he earned?
The amount of interest he has earned is $438
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
A = P ( 1+r/100) ^t
A is the amount after year t
P is the principal and r is the rate
800 = P( 1+ 12/100)⁷
800 = P( 1+ 0.12)⁷
800 = P ( 1.12)⁷
800 = P( 2.21)
P = 800/2.21
P = $362
A = P+ 1
I = A-P
I =800 - 362
I = $438
therefore the interest he earned is $438
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Find the value of each variable please show proofs
Tell whether the ordered pair is a solution of the equation.
7=y-5× (4,28)
Answer: No
Step-by-step explanation:
So you have to substitute the x and y with the numbers in the ordered pair.
y becomes 28.
x becomes 4.
So the equation 7 = y - 5x becomes 7 = 28 - 5(4).
Then, you solve.
7 = 28 - 5(4)
7 = 28 - 20
7 = 8
7 ≠ 8
So, the ordered pair is NOT a solution of the equation.
Hope this helps!!!
Write the equation of a rational function that has been translated left 2 units and shifted up 1 unit.
The equation of a rational function that has been translated left 2 units and shifted up 1 unit is; f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
What is the equation after transformation?A relation is defined as a function in the event that it possesses only One y-value with a corresponding x-value.
A general form of how a rational function is represented is:
f(x) = (ax + b) / (cx + d)
To translate this function left 2 units, we need to replace x with x + 2. This gives us:
f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)
To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:
f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)
Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
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Given: Prove: Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (0, b) at (0, 6) and blue line s intercepts (c, 0) at (2, 0) and (0, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality Which step of the proof contains an error? A. Step 6 B. Step 4 C. Step 2 D. Step 5
The two lines are intercept of each other and can intersect each other and are perpendicular to each other.
With examples, what is line intercept sampling?
To calculate the cover of specified classes in the landscape, such as forests or different types of forests, line intercept sampling is utilized.
Over the region of interest, line samples are randomly placed, and it is then examined what percentage of each sample line falls into the target area class.
The points at which a line crosses an axis are known as the xxx-intercept and the yyy-intercept, respectively.
Thus, the two lines are intercept of each other and can intersect each other and are perpendicular to each other.
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Let y=f(x), where
f(x)=x^5 -8x.
Find the differential of the function.
dy=
The differential of the function, f(x)=x^5 -8x is
df(x) = (5x^4 - 8) dx. That is dy = (5x^4 - 8) dx
Determining the differential of the given functionFrom the question, we are to determine the differential of the given function
To find the differential of the function f(x), we use the formula:
df(x) = f'(x) dx
where f'(x) is the derivative of f(x) with respect to x, and dx is an infinitesimal change in x.
First, we need to find the derivative of f(x):
f'(x) = 5x^4 - 8
Now we can substitute this into the differential formula:
df(x) = (5x^4 - 8) dx
Hence, the differential of the function is
df(x) = (5x^4 - 8) dx
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Help help help help I really need help on this question please
Answer:60 cents per taco
Step-by-step explanation:
120/2=60
180/3=60
300/5=60
480/8=60
Helppp! The tree diagram below shows all of the outcomes for flipping 3 coins. Which outcome is represented x? Picture below.
Answer:
Option 1 is the correct choice
Step-by-step explanation:
All possible outcomes are represented with the exception of {HHT}
This would correspond to x
Option 1 is the correct choice
The length of a rectangular poster is 8 more inches than two times its width. The area of the poster is 42 square inches. Solve for the dimensions (length and width) of the poster.
The dimensions of the poster are approximately 10.64 inches by 1.15 inches.
What are dimensions of an objects?
Dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, breadth, and height.
According to the problem, the length of the poster is 8 more inches than two times the width, which can be expressed as:
length = 2x + 8
The area of the poster is given as 42 square inches, so we can set up the equation:
area = length * width
Substituting the expressions for length and width, we get:
42 = (2x + 8) * x
Expanding the right side, we get:
[tex]42 = 2x^2 + 8x[/tex]
Moving all terms to one side, we get:
[tex]2x^2 + 8x - 42 = 0[/tex]
Dividing both sides by 2, we get:
[tex]x^2 + 4x - 21 = 0[/tex]
We can solve for x using the quadratic formula:
x = (-4 ± √(4² - 41(-21))) / (2*1)
x = (-4 ± √88) / 2
x = (-4 ± 2√22) / 2
x = -2 ± √22
Since the width of the poster cannot be negative, we take the positive solution:
x = -2 + √22
Using this value, we can find the length of the poster:
length = 2x + 8 = 2(-2 + √22) + 8 = 2√22 + 4
Therefore, the length of the poster is approximately 10.64 inches (rounded to two decimal places).
Thus, the dimensions of the poster are approximately 10.64 inches by 1.15 inches.
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Determine which of the following features they have in common.
The range for both of the plots is same.
What is the domain and range of function?A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain.
The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.
Use the graphs of f(x)= and g(x) =3/x+3, log2(x+3) to determine which of the following x+3 features they have in common.
The range is the same for all the plots.
For both cases the range is (-∞,∞)
Hence The range for both of the plots are same.
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a flower nursery grows daisies 4/10 of the days is our golden color 8/10 of the gold days is are ready to cut which model shows the fraction of days is that are gold and ready to cut
The day she will order both kinds of flowers on the same day is 12th day of the year.
What is LCM?LCM is the full form of least common multiple, it stands for the lowest common multiple. The least common multiple of two numbers can be mentioned as the smallest number that is a multiple of both of them.
here, we have,
Given:
Sunflower order = every 6 days
Daisies order = every 4 days
Find the lowest common multiple of 6 days and 4 days
6 days = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
4 days = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
The lowest common multiple of 6 days and 4 days is 12 days
Therefore, the day she will order both kinds of flowers on the same day is 12th day of the year.
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a box of whole wheat spaghetti contains 8 servers and has 28 grams of fiber
(x - 1) ^ 7 -( x -1) ^ 4
Answer: The number that makes this number sentence true is ______. Fill in the blank. Look at the picture.
Answer:25
Step-by-step explanation:39+26=65,
65-40=25,
39+26=25+40
Answer:
Step-by-step explanation:
65-40=25,
39+26=25+40
The net of a triangular prism and its dimensions are shown below. What is the total surface area of the prism? The net of a triangular prism and its dimensions are shown below.
What is the total surface area of the prism?
The total surface area of the prism is equal to 74 m².
How to calculate the total surface area of the triangular prism?In Mathematics, the total surface area of a triangular prism can be calculated by using this mathematical expression:
Total surface area of triangular prism = (Perimeter of the base × Length of the prism) + (2 × Base area)
Total surface area of triangular prism = (S₁ + S₂ + S₃)L + bh
where:
b is the bottom edge of the base triangle.h is the height of the base triangle.L is the length of the triangular prism.S₁, S₂, and S₃ represent the three sides (edges) of the base triangle.By substituting the given parameters, we have:
Total surface area of triangular prism = 4 + (5 × 4)3.5
Total surface area of triangular prism = 4 + (20)3.5
Total surface area of triangular prism = 74 m².
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A teacher assigns five students a rational expression to translate into an equivalent radical expression. The table shows the students’ responses.
49^{1/2} and (8x)^{1/3} are correct in polynomial .
What is a polynomial, simply put?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.
1) [tex]49^{1/2}[/tex] = √49
4) [tex](8x)^{1/3}[/tex] = ∛8x
option 1 and 4 is correct.
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Consider the given system of equations. How many (x,y) solutions does this system have ? 2x+4y=15
2x+4y=13
Answer:It has no solution
Step-by-step explanation:
in need of help! thank you in advance
Answer:
1. 12
2. 6
3. 4.5
4. 7
Don't quite under #5
Explanation:
Sample mean = ΣX / n
1. 108 / 9 = 12
2. 72 / 12 = 6
3. 2 + 7 + 9 + 4 + 5 + 3 + 0 + 6 = 36 / 8 = 4.5
4. 8 + 2 + 5 + 7 + 12 + 9 + 11 + 3 + 6 = 63 / 9 = 7
The two figures below are similar figures.
Which proportion must be true?
Select two correct answers.
The proportion is (y/x) = (26/20).
What are Similar Triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
As per the given data:
Two figures below are similar figures.
All sides are given in the diagram.
If any two triangles are similar, then their corresponding sides are in the same proportion.
∴ (2.5 / x) = (1 / 1.5) = (3.25 / y)
= (5/2x) = (2/3) = (13/4y)
From cross-multiplication, we can find:
(y/x) = (26/20)
Hence, the proportion is (y/x) = (26/20).
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MATH I WILL GIVE BRAINLIEST!
d ≥ 4, The family must travel at least four days.
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is replaced by less than (or less than or equal to), more than (or greater than or equal to), or not.
Given:
The family drives 350 miles per day.
they need to travel at least 1400 miles
let the number of day taken to travel 1400 miles.
So, the Inequality of the Situation as
350d ≥ 1400
d≥ 1400/350
d≥ 140/ 35
d ≥ 4
So, the family must travel at least four days.
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Find P(5.5 ≤ X ≤ 7.5) where x is normally distributed with mean μ = 2.6 and standard deviation σ = 2.2
Therefore, the probability that X is between 5.5 and 7.5 is approximately 0.0808.
An illustration of a distribution is what?If a company creates apparel and sells it to people directly through an online site, it may be using direct distribution.
To solve this problem, we need to standardize the distribution of X to a standard normal distribution. This is done using the following formula:
Z = (X - μ) / σ
where Z is the standard normal variable, X is the normally distributed variable, μ is the mean of X, and σ is the standard deviation of X.
Using the given values, we have:
Z1 = (5.5 - 2.6) / 2.2 = 1.318
Z2 = (7.5 - 2.6) / 2.2 = 2.682
We can then find the probability using the standard normal distribution table or a calculator with a built-in normal distribution function.
Using the table or calculator, the probability is:
P(5.5 ≤ X ≤ 7.5) = P(1.318 ≤ Z ≤ 2.682) = 0.0808 (rounded to four decimal places)
Therefore, the probability that X is between 5.5 and 7.5 is approximately 0.0808.
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A photocopier enlarges in the ratio 7:4 what would be the new size of a diagram measuring 16 cm and 12cm?
Answer:
The new size of the diagram would be 28 cm by 16.8 cm. This is calculated by multiplying the original dimensions of 16 cm and 12 cm by the ratio of 7:4. Therefore, the new width of the diagram would be 16 cm x 7 = 112 cm and the new height would be 12 cm x 4 = 48 cm. The new size of the diagram is therefore 112 cm by 48 cm, which can be simplified to 28 cm by 16.8 cm
Step-by-step explanation:
A photocopier that enlarges in the ratio 7:4 will increase the size of the diagram by a factor of 7/4. To find the new size of the diagram, we can multiply the original measurements by the factor of enlargement.
The new width of the diagram will be:
16 cm × 7/4 = 28 cm
The new height of the diagram will be:
12 cm × 7/4 = 21 cm
Therefore, the new size of the diagram will be 28 cm by 21 cm.
Answer: The new size of the diagram will be 28 cm by 21 cm.
1.1 PQR is a tangent to circle QABCD. AB is parallel to QD and CD = CB. Ĉ= 110°; D3= 70° and ₂= 100°. P Cloo Determine with reasons the sizes of the following: 1.1.1 B₁ (3) 1.1.2 ABC (4) 1.1.3 D₂ (2) 1.1.4 A₂
Answer: Unfortunately, the given information is not sufficient to answer the questions 1.1.1, 1.1.2, 1.1.3, and 1.1.4. However, I can provide some insights based on the given information.
1.1.1: B₁ is not defined in the given information. Without knowing what B₁ represents, we cannot determine its size.
1.1.2: We know that AB is parallel to QD, and CD = CB. Also, angle Ĉ = 110°. However, we don't know the location of point P, so we cannot determine the size of angle ABC.
1.1.3: We know that angle D₃ = 70°, but we don't know the location of point P, so we cannot determine the size of angle D₂.
1.1.4: We know that angle ₂ = 100°, but we don't know the location of point P, so we cannot determine the size of angle A₂.
Step-by-step explanation:
In ΔRST, s = 85 inches, mm∠S=28° and mm∠T=87°. Find the length of t, to the nearest inch.
Answer:
181
Step-by-step explanation:
Answer:
181
Step-by-step explanation:
Just Cause.
Francine has cut a piece of paper into a triangle but did not make a perpendicular cut find the area of piece of paper to the nearest tenth of a square centimeter
Answer: Without a perpendicular cut, we cannot determine the height of the triangle directly. However, we can use the Pythagorean Theorem to find it indirectly.
Let's assume that Francine has cut the paper into a right triangle ABC, where AB and BC are the legs of the triangle, and AC is the hypotenuse. Let x be the length of AB and y be the length of BC. We can then use the Pythagorean Theorem to find the length of AC:
AC^2 = AB^2 + BC^2
We don't know the exact values of AB and BC, but we do know that the area of the triangle is given by:
Area = (1/2) * AB * BC
We can use this formula to find the area in terms of x and y:
Area = (1/2) * x * y
Now we need to eliminate one of the variables (either x or y) so that we can express the area in terms of the other variable and AC. We can do this by rearranging the Pythagorean Theorem to solve for one of the variables:
x^2 = AC^2 - y^2
y^2 = AC^2 - x^2
Let's solve for y:
y^2 = AC^2 - x^2
y = sqrt(AC^2 - x^2)
Now we can substitute this expression for y into the formula for the area:
Area = (1/2) * x * sqrt(AC^2 - x^2)
To find the maximum possible area, we need to maximize this expression. We can do this using calculus, by taking the derivative of the expression with respect to x, setting it equal to zero, and solving for x. However, since we only need an approximate answer to the nearest tenth of a square centimeter, we can use trial and error to find the value of x that gives the maximum area. We can start by trying different values of x, and using a calculator to evaluate the expression and find the corresponding area.
Let's try a few values of x:
If x = 0, then the area is 0.
If x = AC/2 (i.e., if the triangle is isosceles), then the area is (1/8) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.
If x = AC/sqrt(3) (i.e., if the triangle is equilateral), then the area is (1/4) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.
Since the area is maximized when the triangle is equilateral, we can assume that the piece of paper is an equilateral triangle, and use the formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
where side is the length of one of the sides of the triangle. To find the side length, we need to know the length of AC. We don't know the exact value of AC, but we can estimate it by measuring the length of the longest side of the piece of paper (assuming that it is the hypotenuse of the triangle). Let's say that the longest side is 30 cm. Then, by the Pythagorean Theorem, we can find the length of the other two sides:
x^2 + y^2 = 30^2
x^2 + (sqrt(AC^2 - x^2))^2 = 30^2
2x^2 + AC^2 - x^2 = 900
x^2 = (900 - AC^2)/
Step-by-step explanation:
You go into a car dealership and tell them that you have a budget of $300/month. You are interested in getting a Chevy Cruze that is on sale for $16,000. Due to your excellent credit score, you qualify for a 5-year loan at 4% APR with No Down Payment. What is your monthly payment? Are you within budget?
how much will the car cost you after the loan has been paid in full?
Answer: $17,788.20
Step-by-step explanation:
To calculate the monthly payment, we can use the loan formula:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P is the monthly payment
A is the loan amount, which is the sale price of the car ($16,000) in this case
r is the monthly interest rate, which is the annual percentage rate (APR) divided by 12 (4% / 12 = 0.003333...)
n is the total number of payments, which is the number of years of the loan multiplied by 12 (5 years * 12 = 60)
Substituting these values into the formula, we get:
P = (0.003333... * $16,000) / (1 - (1 + 0.003333...)^(-60))
P ≈ $296.47
Therefore, the monthly payment is approximately $296.47, which is within the budget of $300/month.
To calculate the total cost of the car after the loan has been paid in full, we can multiply the monthly payment by the total number of payments (60) and add the original sale price of the car:
Total cost = P * n + A
Total cost = $296.47 * 60 + $16,000
Total cost = $17,788.20
Therefore, the total cost of the car after the loan has been paid in full is approximately $17,788.20.