The passing score of the student when the standard deviation and mean are given is calculated to be 111.1.
Standard deviation = 17
Mean = 120
Percentage of students failed in the exam = 30%
Let us find Z such that P(Z< (X - 120)/17) = 0.3
By referring the table, the Z value corresponding to 0.3 probability is observed to be -0.525.
This means that (X - 120)/17 = -0.525
(X - 120) = 17 × -0.525
(X - 120) = -8.925
X = 120 - 8.925 = 111.07 ≈ 111.1
Thus, the required passing score is calculated to be 111.1.
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Line segment SU is dilated to create S'U' using the dilation rule DQ,2. 5. What is the distance, x, between points U' and U?
4 units
4. 8 units
6 units
10 units
If Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , then the distance "x" between points U' and U is (c) 6 units .
The Scale Factor is written as ratio of the distance from center to image of a point and distance from center to corresponding point.
the scale factor from the figure can be written as : QU'/QU ;
From the figure , we can see that QU = 4 units and scale factor is = 2.5 ;
⇒ 2.5 = QU'/4 ;
On simplifying ,
we get ;
⇒ QU' = 2.5 × 4 = 10 ;
From the figure : UU' = QU' - QU ;
⇒ UU' = 10 - 4 = 6 .
Therefore , the distance between points U and U' denoted by "x" is 6 units .
The given question is incomplete , the complete question is
Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , What is the distance, x, between points U' and U?
(a) 4 units
(b) 4.8 units
(c) 6 units
(d) 10 units
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A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately
1290 deer in the population. Which function can be used to determine the number of deer, y, in this population
at the end of t years?
The function is y = 1500[tex](0.985)^t[/tex].
What is function?
A mathematical function , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here initial population is 1500 .
Rate of decrease = 1.5%
Number of years = 10
After 10 years , the end population = 1290.
Now using formula,
=> P = [tex]P_0[/tex][tex](1-\frac{r}{100})^n[/tex]
Here number of deer, y, in this population at the end of t years then
=> y = 1500[tex](1-\frac{1.5}{100})^t[/tex]
=> y = 1500[tex](1-0.015)^t[/tex]
=> y = 1500[tex](0.985)^t[/tex]
Hence the function is y = 1500[tex](0.985)^t[/tex].
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i need a help with graphing
A graph of the line that passes through the two points (-3/2, -3/2) and (3/2, 3/2) is shown in the image attached below.
How to calculate the slope of any straight line?In Mathematics and Geometry, the slope of any straight line can be calculated by using this mathematical equation (expression);
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points located on the line:
Points on the x-coordinate = (-3/2, 3/2).
Points on the y-coordinate = (-3/2, 3/2).
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (3/2 + 3/2)/(3/2 + 3/2)
Slope (m) = 3/3 = 1
At point (-3/2, -3/2), an equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.c represents the intercept.y - (-3/2) = 1(x - (-3/2))
y + 1.5 = x + 1.5
y = x
Next, we would use an online graphing calculator to plot the linear equation as shown in the graph attached below.
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3
The teacher estimated that she would have 68 students this school year. She actually had 74.
What is the percent error?
A 2. 08%
B
6%
8. 11%
D 191. 89%
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
The answer is C
Hope this helped!
Please can somebody help me do this further maths gcse question in ‘transformations of graphs and functions’
Answer:
y=f(x)-6 is a vertical translation down by 6 units so draw the same graph but 6 units down with the point at which it crosses the y-axis as (0,-4)
An item on sale costs 30% of the original price. If the original price was $90 what is the sale price
state which theorem you can use to show that the quadrilateral is a parallelogram
Answer:
opposite angles are equal and parallel
For the following right traingle, find the side length x. Round your answer to the nearest hundredth
7.21
Step-by-step explanation:The Pythagoras theorem allows us to solve for unknown sides of right triangles.
Right Triangles
Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.
Pythagorean Theorem
The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.
12² + b² = 14²Then, subtract 12² from both sides.
14² - 12² = b²52 = b²Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.
7.21 ≈ bYour friend
finds the sum. Is your friend correct?
Explain your reasoning.
-3.7 + (-0.25) = | 3.7 | + | 0.25 | = 3.7 + 0.25 = 3.95
Answer:
Yes, the friend is correct in finding the sum of -3.7 + (-0.25) = 3.95.
To find the sum, the friend first takes the absolute value of each number (ignoring the negative sign) to find that the absolute value of -3.7 is 3.7 and the absolute value of -0.25 is 0.25.
Then, the friend adds the absolute values of the numbers (3.7 + 0.25) to get 3.95 which is the final answer.
The order of operation is correct and the arithmetic is also correct, so the final result is the correct sum of the two given numbers.
Your water hose leaking at a rate of 0.25 cups per hour. How many gallons did your hose leak in a full 24 hour day ?
well, let's first find out how many cups was that in 24 hours anyhow.
so in 1hr the hose leaks 0.25 cups, so in 24 hrs that'd be (24)(0.25) = 6 cups.
Since a gallon has 16 cups, that'd be 6/16 gallons or 3/8 = 0.375 of a gallon.
Help please help please
Answer:
x = 60.4
Step-by-step explanation:
First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.
[tex]cos(22) = \frac{56}{x}[/tex]
We need to set up a proportion because there is not much else you could do here.
[tex]\frac{cos(22)}{1} =\frac{56}{x}[/tex]
Then, cross-multiply.
[tex]cos(22) * x = 56[/tex]
Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!
[tex]\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}[/tex]
[tex]x = 60.4[/tex]
Rounded to the nearest tenth, x = 60.4.
Jenny went for a drive in her new car. She drove for 198.4 miles at a speed of 62 miles per hour. For how many hours did she drive?
The number of hours that Jenny drove in her new car is 3.2 hours
How to calculate the number of hours that Jenny drove in her car?
The speed is 62 miles
The distance is 198.4 miles
The number of hours can be calculated as follows
speed= distance/time
62= 198.4/x
cross multiply both sides
62x= 198.4
x= 198.4/62
x= 3.2
Hence the number of hours that Jenny drove is 3.2 hours
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(−4x + 3)(−2x2 − 8x + 2)
On solving the expression, the standard form is obtained as 8x³ + 26x² - 32x + 6.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - (−4x + 3)(−2x² − 8x + 2)
To solve this expression first expand the equation using arithmetic operation of multiplication.
(−4x + 3)(−2x² − 8x + 2)
-4x(−2x² − 8x + 2) + 3(−2x² − 8x + 2)
8x³ + 32x² - 8x - 6x² - 24x + 6
Collect the like terms together -
8x³ + 32x² - 6x² - 8x - 24x + 6
Perform the arithmetic operation of addition and subtraction -
8x³ + 26x² - 32x + 6
Therefore, the standard form is 8x³ + 26x² - 32x + 6.
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Quadrilateral EFGH is a rectangle. If m∠FEG=57° , find m∠GEH .
The measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
Define the term compliment angles?When two angles sum up to 90 degrees, they are complementary (a Right Angle).Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees & 60 degrees, for instance, are complimentary angles.They don't even have to be close to one another for the total to be 90 degrees.Examples:
The complimentary angles of 40° and 50°.The complementary angles of 60° and 30° are.The corresponding angles of 5° and 85° are.For this stated question:
In the rectangle EFGH.
m∠FEG=57°
Then,
m∠FEG + m∠GEH = 90 (complimentary angles)
57° + m∠GEH = 90
m∠GEH = 90 - 57
m∠GEH = 33°
Thus, the measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
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Find the selling price.
Cost to store: $65
Markup: 80%
The selling price for the article if it is equal to marked price will be $117
using profit and loss formulas.
What is profit and loss formula?
Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. The important terms covered under this are cost price, fixed, variable and semi-variable cost, selling price, marked price, list price, margin, etc.
For example, for a shopkeeper, if the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss.
Now,
Given Cost price=$65
Marked up price = 180%*$65
As
Marked up price = selling price
Therefore
selling price= 180%*$65
selling price =$117
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please help me with my homework!
Answer:
The machine makes 45 bottles per minute.
Step-by-step explanation:
We can first find the slope through this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]
Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:
[tex]\frac{315-90}{7-2}[/tex]
= 45
Therefore, m = 45.
Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line: [tex]y-y1 = m(x-x1)[/tex]
For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:
y - (90) = 45(x - 2)
We can solve for y now to find what y=mx+b is:
y = 45(x-2) + 90
y = 45x
Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45
The machine makes 45 bottles per minute.
find the area of region s . find the volume of the solid generated when region s is revolved about the horizontal line y
The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.
We have to find the volume of the solid generated when region s is revolved about the horizontal line y.
As shaded region is revolved around y = -3.
Outer radius = f(x) + 3
Inner radius = g(x) + 3
Width = dx
Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.
dv = π[tex](f(x) + 3)^3[/tex]dx - π[tex](g(x) + 3)^2[/tex]dx
dv = π([tex]f^2[/tex](x) + 6f(x) + 9)dx - π([tex]g^2[/tex](x) + 6g(x) + 9)dx
dv = π([tex]f^2[/tex](x) + 6f(x))dx - π([tex]g^2[/tex](x) + 6g(x))dx
Now integrating on both side:
[tex]\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125[/tex]
Using the provided result or a scientific calculator, the entire definite integral was discovered.
v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125
v = 93.04919
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The complete question is given below:
I Need help with this I’ve tried stuff and stuff but it’s not working
Answer:
y= -2x + 0
Step-by-step explanation:
to get to y you need to multiply by -2 and add 0 to that to get the final y answer
Combine like terms to create an equivalent expression.
3.4 2.8d +2.8d-1.3
Answer:
Step-by-step explanation:
If the problem was supposed to be "3.4 + 2.8d + 2.8d -1.3". Then the answer would be 5.6d + 2.1. you can combine the "d" terms because they have the same variable and you can combine the number terms because they are like. This result in 2.8d+2.8d + 3.4 - 1.3. This simplifies to the correct answer given above.
Roger received $200 for his birthday. He wants to use the money to buy new clothes for work. He can buy pants
for $30 and shirts for $20. He wants at least 6 new items. Determine the shirt and pants combination Roger
can buy.
From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.
He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:
30x + 20y ≤ 200 (1)
Also:
He wants at least 6 new items. hence:
x + y ≥ 6 (2)
From both equations, the solution to these equalities is (3, 3)
Roger can buy 3 pants and 3 shirts.
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area of the segment?
Answer:
A ≈ 34.91 m²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{40}{360}[/tex] ( r is the radius )
= π × 10² × [tex]\frac{1}{9}[/tex]
= [tex]\frac{100\pi }{9}[/tex]
≈ 34.91 m² ( to 2 decimal places )
Answer:
34.88m²
(round 35m²)
Step-by-step explanation:
a round angle, that of the circle, is 360°, here we have a portion of 40°, we divide 360° by 40° and we have the percentage with respect to the circle
360° : 40° = 9
we now know that the wedge is 1/9 of the circlefind the area of the whole circle having the radius (10m)Area of Circle Formulas · Area = π × r2, where 'r' is the radius
Area = π × r2
Area = π × 10²
Area = π × 100
Area = 3.14 × 100
Area = 314 m²
now we divide by 9 and we have the area of the wedge314 : 9 = 34.88m² (round 35m²)
Using y = 6 - 2x, plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear. Part 1 out of 3 Complete the table. Input, x Output, y Check -1 3 Next
Answer:
.................................................................................
Step-by-step explanation:
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ok
Think about what you know about breaking apart numbers with addition. Fill in each box. Use words, numbers. and picture. Show as many ideas as you can.
The breaking of number using addition is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the breaking apart of numbers with addition.
We can breaking apart the numbers with addition as follows. Assume the number to be 50. We can break the number 50 as follows -
50 = 25 + 25
50 = 15 + 10 + 15 + 10
50 = 10 + 10 + 10 + 10 + 10
50 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
Therefore, the breaking of number using addition is discussed above.
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I believe A and C are part of the answer but I am unsure of the rest
Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;
B.
What is an enlargement transformation?An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.
An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.
Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.
The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B
Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word
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What is the equation of the line that passes through the point (-3,-8) and has a slope of 0
Answer:
The equation of a line in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
Given a point and the slope, we can find the equation of the line that passes through that point. We know that the slope of the line is 0, so we can write the equation of the line as:
y = 0x + b
We also know that the line passes through the point (-3,-8), so we can substitute these values into the equation and solve for b, the y-intercept:
-8 = 0(-3) + b
-8 = 0 + b
b = -8
So the equation of the line that passes through the point (-3,-8) and has a slope of 0 is:
y = 0x - 8
This line is a horizontal line with y-intercept -8, which means that the line passes through the point (0,-8)
100 points Factor completely and then place the factors in the proper location on the grid. 4 y2 + 25 y + 6
The factored expression to the expression is (4y + 1)(y + 6)
How to determine the factor to the equationFrom the question, we have the following parameters that can be used in our computation:
4 y2 + 25 y + 6
Express properly
So, we have the following representation
4y² + 25 y + 6
Expand the expression
This gives
4y² + 24y + y + 6
Next, we factor the expression
4y(y + 6) + 1(y + 6)
Factor out y + 6
(4y + 1)(y + 6)
Hence, the solution is (4y + 1)(y + 6)
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If 3+x<5 and 8+x>5,What range of values of x satisfies both inequalities?
The range of values of x which satisifies both of the inequalities is:
(-3, 2)
What range of values of x satisfies both inequalities?Here we have two inequalities:
3 + x < 5
8 + x > 5
And we want to see which range of values of x satisfie both of these inequalities.
If we isolate x on both inequalities, we will get:
3 + x < 5
x < 5 - 3
x < 2
And the other one is:
8 + x > 5
x > 5 - 8
x > -3
Then we havethe compound inequality:
x < 2
x > -3
Then the range of values that satisfies both inequalities is (-3, 2)
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-13, -17, -21, -25 write an equation for the nth term of the arithmetic sequence then find a10
The tenth term of the given arithmetic sequence is; -49
What is the nth term of an arithmetic sequence?The formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
From the given sequence, we see that;
a = -13
d = -17 - (-13)
d = -17 + 13
d = -4
Thus, the tenth term of the arithmetic sequence is;
a₁₀ = -13 + (10 - 1)-4
a₁₀ = -13 -36
a₁₀ = -49
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e
5 Louay wants a cap with less than white
stars. Which cap could Louay buy?
Cap 1
Cap 1 only
Cap 2 only
C
Cap 2 or 3
D Cap 1 or 3
A
B
Cap 2
Cap 3
The correct option regarding which cap Louay can buy is given as follows:
D. Cap 1 or 3.
How to obtain the fraction of white stars?The fraction of white stars is obtained using a proportion, dividing the number of white stars by the total number of stars.
Hence the fractions for each cap are given as follows:
Cap 1: 1/3 = 0.33 < 1/2 = 0.5.Cap 2: 2/4 = 0.5 = 0.5.Cap 3: 2/5 = 0.4 < 1/2 = 0.5.Meaning that Cap 1 and Cap 3 have the desired ratio of white stars relative to total stars, and thus the correct option is given by option D.
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(PLEASE HELP) At a local print shop, 15 copies can be made for $6. At this rate, how much would it cost to make 35 copies???
Answer:
14 dollars
Step-by-step explanation:
They vary in direct proportion
Thus; If 15 copies = 6dollars
35 copies = (35 × 6) ÷ 15
= 210 ÷ 15
= 14
It would cost 18$
Every fifteen copies you have to pay 6$, and since 35 is 3 times 15, it would also be 3 times the price, or 6 * 3$ which equals 18$