Answer:
£481.02
Step-by-step explanation:
To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:
£466.98 * 1.032 = £480.9936
£480.9936 + £466.98 = £481.02
Rounding to 2 decimal places, the answer is £481.02.
What value of x makes the equation
3(x - 5) - 7 = 2 true?
Answer:
x=8
Step-by-step explanation:
We can first take out 3(x-5) and expand it into: (3*x) + (3*-5) = 3x-15
Now, let's plug it into the original equation:
3x-15-7 = 2
Let's solve for x:
3x = 2+15+7
3x = 24
x = 8
Bob has 60 coins consisting of quarters and dimes. The coins combined value is
$13.35. How many quarters and how many dimes does he have?
O q+d= 13.35
0.25g +0.10d = 60
Oq-d=13.35
O
0.25g +0.10d = 60
q+d=60
0.25g +0.10d = 13.35
.25g + d = 60
q+0.10d 13.35
=
Answer:
Third option
q + d = 60
0.25q + 0.10d = 13.35
Step-by-step explanation:
Given q quarters and d dimes
Total number of coins = q + d and this must equal 60
Therefore q + d = 60
Since each quarter is 25 cents(or $0.25) and each dime is 10 cents($0.10)
Total value = 0.25q + 0.10d = 13.35
Correct set of equations is the third option
2n × r × 2 × 1 × s
for n = 2, r = 2, and s = 1.
there are 4 teachers for every 100 students at Brians school. if there are 950 students, write and solve a proportion showing how many teachers are at the school
Step-by-step explanation:
We can set up the proportion with students on the bottom and teachers on the to
[tex] \frac{4}{100} = \frac{x}{950} [/tex]
Now we cross multiply
[tex]100x = (950)(4)[/tex]
[tex]100x = 3800[/tex]
Lastly, we will divide both sides by 100
[tex]x = 38[/tex]
streets that form a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.
The area of the square block is 48,881 m2, which is calculated by multiplying the length of each side (221 m) by itself.
The area of a square can be calculated by multiplying the length of one side by itself. In this case, the length of each side is 221 m. To find the area of the square block, we need to multiply 221 m by itself. This gives us 48,881 m2 as the final answer. To summarize, the area of the square can be found by multiplying the length of one side by itself. In this case, the length of each side of the block was 221 m, so 221 m multiplied by 221 m results in a total area of 48,881 m2.
The complete question: In one city there are four straight streets that form a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.
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g- given that a part produced in the plant is defective, what is the probability that it went through an electronic inspection?
The probability that a defective part went through an electronic inspection is 0.2058 or approximately 20.58%.
In order to find the probability that a defective part went through an electronic inspection, Bayes' Theorem will be used. The theorem states that the conditional probability of event A given event B can be calculated as:
P(A | B) = P(B | A) × P(A) / P(B)
where P(A) is the prior probability of event A, P(B | A) is the conditional probability of event B given event A, and P(B) is the overall probability of event B.
In this case, event A is the part that went through an electronic inspection, and event B is the part that is defective. The prior probability of a part going through an electronic inspection is:
P(A) = 0.15, and the overall probability of a part being defective is P(B) = 0.15 × 0.97 + 0.85 × (1 - 0.15) = 0.14695.
The conditional probability of a part being defective given it went through an electronic inspection is P(B | A) = 0.03. The probability of a part that went through an electronic inspection given it's defective is:
P(A | B) = P(B | A) × P(A) / P(B) = 0.03 × 0.15 / 0.14695 = 0.2058
So, the probability that a defective part went through an electronic inspection is 0.2058 or approximately 20.58%.
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Question
At a plant, 30% of all the produced parts are subject to a special electronic inspection. It is known that any produced part which was inspected electronically has no defects with probability 0.15. For a part that was not inspected electronically this probability is only 0.85. What is the probability that it went through an electronic inspection?
three vectors have equal magnitudes and make 120° with each other. we can say that
the magnitude of the resultant is [tex]\sqrt{2}[/tex] times the magnitude of each individual vector, not one-third.
No, that is incorrect. The magnitude of the resultant of three vectors having equal magnitudes and making an angle of 120 degrees with each other is not one-third the magnitude of the component vectors.
The magnitude of the resultant of three vectors depends on the angle between them, as well as their magnitudes. In general, the magnitude of the resultant of three vectors can be calculated using the law of cosines, which states that the square of the magnitude of the resultant (R^2) is equal to the sum of the squares of the magnitudes of the individual vectors ([tex]A^2, B^2, and C^2[/tex]), plus twice the product of the magnitudes of two of the vectors multiplied by the cosine of the angle between them.
For three vectors of equal magnitude (A = B = C = m), the magnitude of the resultant can be calculated as:
[tex]R^2 = 3m^2 + 2m^2 * cos(120) = 3m^2 - m^2 = 2m^2[/tex]
[tex]R = \sqrt{2} * m[/tex]
Therefore, the magnitude of the resultant is sqrt(2) times the magnitude of each individual vector, not one-third.
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Question: Three Vectors Have Equal Magnitudes And Make 120° With Each Other. We Can Say That The Magnitude Of The Resultant Is One-Third The Magnitude Of The Component Vectors. The Resultant Is Zero. The Magnitude Of The Resultant Is Equal To The Magnitude Of The Component Vectors. The Magnitude Of The Resultant Is More Than Three Times The Magnitude Of Each component Vector.
what is 10% of £7.50
Answer: 0.75 :D Hope this helps
Step-by-step explanation:
last year, 20 percent of all teenagers purchased a new iphone. this year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iphone. to test whether the percentage has decreased, the p-value is:
The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.
The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.
Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
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Match the exponent expression with it's correct solution.
According to algebra property of power of a power, the following results are listed below:
Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)
Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)
Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)
Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)
How to apply power properties
In this question we find four cases of power of a power, whose solution is described by the following algebra property:
(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.
Now we proceed to determine the solution to each case:
Case 1
(x⁵)³ = x¹⁵
Case 2
(x⁸)⁷ = x⁵⁶
Case 3
(x⁷)¹⁰ = x⁷⁰
Case 4
(x¹⁴)³ = x⁴²
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What is the arc measure of major arc BAC in degrees?
Answer:
arc BAC = 276°
Step-by-step explanation:
the sum of the angles around point D is 360°
sum the central angles and equate to 360
7n + 12 + 6n + 13n - 16 = 360
26n - 4 = 360 ( add 4 to both sides )
26n = 364 ( divide both sides by 26 )
n = 14
Then
∠ ADB = 7n + 12 = 7(14) + 12 = 98 + 12 = 110°
∠ ADC = 13n - 16 = 13(14) - 16 = 182 - 16 = 166°
• the arc of a circle is equal to the central angle it subtends
arc BA = ∠ ADB = 110°
arc AC = ∠ ADC = 166°
Then
arc BAC = arc BA + arc AC = 110° + 166° = 276°
Create a flowchart proof of a two column proof. If HG = KG and HI || KJ, prove that HI = KJ
Answer:
Both triangles are congruent by S A S congruent.
Step-by-step explanation:
Congruent triangles:In ΔHIG & ΔKJG,
HG = KG Given
∠GHI ≅ ∠GKJ Alternate interior angles, HI // KJ and KH is transversal
HI = KJ Given
ΔHIG ≅ ΔKJG Side Angle Side congruency
histograms can be used to multiple select question. observe the spread or the variability of the data. observe individual data points. construct a pie chart. determine the shape of the data.
Histograms are commonly used to visualize the distribution of a dataset by grouping the data into bins and representing the frequency of each bin by the height of a bar.
They are useful for observing the spread or variability of the data and determining the shape of the data, such as whether it is symmetrical or skewed. They cannot be used to observe individual data points, but they provide a good visual representation of the overall pattern of the data. Histograms are not appropriate for multiple choice questions as they do not display individual data points in a clear manner. To display parts of a whole, pie charts are a better choice as they show the proportion of each category as a sector of a circle
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In the diagram below,
m∠CIH=100 and m∠BGD=42 Find m∠FHG.
m∠FHG is given as 120 degrees
How to solve for the angle100 + ∠FJG = 180 degrees
∠FJG = 80 degrees
∠BGD = ∠AGJ They are vertically opposite
∠HGI + ∠GIH + ∠IHG = 180
40 + 80 + ∠IHG = 180
∠IHG = 60 degrees
∠IHG + m∠FHG = 180 degrees
60 + m∠FHG = 180
m∠FHG = 120 degrees
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please help, show your work first then choose the answer, thank you
Answer:your mom
Step-by-step explanati
A winter sports pass at Wood Middle School costs $18. A student without a pass must pay
$1.90 for each event. How many sports events would a student have to attend to make the pass a
better deal?
What is the slope of the line below?
PLEASE HELP ME ASAP
Answer:
the answer is E
Step-by-step explanation:
your welcome
A family wants to rent a car to go on vacation. Company A charges $35.50 and 9¢ per mile. Company B charges $65.50 and 13¢ per mile. How much more does Company B charge for x miles than Company A? PLEASE HELPPPP
3004¢ more does Company B charge for x miles than Company A.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
Company A charges $35.50 and 9¢ per mile.
Company B charges $65.50 and 13¢ per mile.
Also, we could convert dollars to cents by multiply it by 100
Since $1 =100 cents.
so, we get,
Company A charges $35.50 and 9¢ per mile. = 3559
Company B charges $65.50 and 13¢ per mile = 6563
difference = 6563 - 3559
= 3004
Hence, 3004¢ more does Company B charge for x miles than Company A.
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Laura ha comprado una falda y una blusa por 66 euros ambas tenian el mismo precio pero en la falda le han hecho un 20% de rebaja y en la blusa solo un 15% ¿cuanto costaba cada prenda?
The cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
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 that Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse.
The cost skirt would be -
${x} = 66 - {20% of 66}
${x} = 66 - {20/100 x 66}
${x} = 66 - {66/5}
${x} = 66 - 13.2
${x} = 52.8
The cost of blouse would be -
${y} = 66 - {15% of 66}
${y} = 66 - {15/100 x 66}
${y} = 66 - {3/20 x 66}
${y} = 66 - 9.9
${y} = 56.1
Therefore, the cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
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{Question in english -
Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse. How much did each item cost??
Elsa is building a fence around her garden. For every 4 feet of fencing, the cost is $2
Complete the table below showing the length of the fence and the cost.
Length of fencing (feet)
Cost ($)
Explanation
Pls help
Answer:
Step-by-step explanation:
4ft : $24 -> 1ft = $6
so 7ft = 6X7 = $42
and 6X10 = $60
what is the solution to 12(x+6)=17
Answer:
x = -55/12
Step-by-step explanation:
12(x+6) = 17
12x + 72 = 17
12x = -55
x = -55/12
Skyla is trying to order the fractions below. Her first step is to rewrite each fraction with a common denominator. What is the lowest common denominator she could use? 17 20 56 8 1
Answer:
Below
Step-by-step explanation:
The lowest common denominator is 60
then the fractions become ( L to right) 51/60 50/60 32/60
A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of ?
The correct response is A since this triangle has a dilatation of (0,0),(1,0),(1,1)) by a factor of 1/3 with respect to the origin.
What is the process of dilation?A figure will dilate if its sides are scaled (multiplied) by the same amount. The scale factor of that dilatation is the name given to that figure.
It is also known as scaling a figure, but since coordinates are involved, it also requires the center of a dilation, which is similar to a pinned point and remains in the same location after dilation.
It appears as though we are adjusting the size of the figure (or leaving it the same when the scale factor is 1).
According to question:The positions (0, 0), (3, 0), (3,3)
1/3 scale factor
Now
the GPS coordinates;
(0,0),(1,0),(1,1)
Thus, required dilation is (0,0),(1,0),(1,1).
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Complete question:
A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of 1/3?
Answer:
The positions (0, 0), (3, 0), (3,3)
1/3 scale factor
Now
the GPS coordinates;
(0,0),(1,0),(1,1)
Thus, required dilation is (0,0),(1,0),(1,1).
Step-by-step explanation:
option a
4. VOLUME The volume of one column of the Lincoln Memorial is approximated by the expression (x³ +37x²-110x + 400). If the height of the column is x + 40 feet, find the expression that approximates the area of the base of the column in terms of x and pi.
To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.
The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.
Using the given expression for the volume of the column, we can write:
πr²h = x³ + 37x² - 110x + 400
Since h = x + 40, we can substitute to get:
πr²(x + 40) = x³ + 37x² - 110x + 400
Dividing both sides by π(x + 40) gives us:
r² = (x³ + 37x² - 110x + 400) / (π(x + 40))
Finally, taking the square root of both sides gives us the expression for the radius in terms of x:
r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))
So, the expression that approximates the area of the base of the column in terms of x and π is:
A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²
2. after 15 hours and 12 minutes a tsunami from krakatau hit port elizabeth, south africa, 7546 kilometers away. find the average speed of the tsunami.
The average speed of the tsunami was approximately 496.45 km/hr.
To find the average speed of the tsunami, we need to know the distance it traveled (7546 kilometers) and the time it took to travel that distance (15 hours and 12 minutes).
First, we need to convert the time to a single unit of measurement. For this calculation, we'll use hours. To do this, we'll convert the minutes to hours:
15 hours + 12 minutes ÷ 60 minutes/hour
= 15.2 hours
Next, we can divide the distance traveled by the time it took:
7546 km ÷ 15.2 hours
= 496.45 km/hr
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Real World Application
Cody and Aliyah are selling wrapping paper for a school fundraise.
Customers can buy rolls of plain wrapping paper and rolls of
holiday wrapping paper. Cody sold 5 rolls of plain wrapping paper
and 8 rolls of holiday wrapping paper for a total of $174. Aliyah
sold 5 rolls of plain wrapping paper and 10 rolls of holiday
wrapping paper for a total of $210. What is the solution to the
system of equations? What is the cost each of one roll of plain
wrapping paper and one roll of holiday wrapping paper?
Roll of plain wrapping paper: $
Roll of holiday wrapping paper: $
Using a system of equations, the unit cost of one roll of plain wrapping paper and one roll of holiday wrapping paper is as follows:
Roll of plain wrapping paper: $6.00Roll of holiday wrapping paper: $18.What is a system of equations?A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.
A system of equations is otherwise known as simultaneous equations.
Plain Wrapper Holiday Wrapper Total Cost
Cody sales 5 8 $174.00
Aliyah 5 10 $210.00
Let the unit cost of Plain Wrapper = x
Let the unit cost of Holiday Wrapper = y
Equations:5x + 8y = 174... Equation 1
5x + 10y = 210... Equation 2
Subtract Equation 1 from Equation 2:
5x + 10y = 210
-
5x + 8y = 174
2y = 36
y = 18
y = $18
Substitute y = 18 in either equation:
5x + 8y = 174
5x + 8(18) = 174
5x +144 = 174
5x = 174 - 144
5x = 30
x = 6
x = $6
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A square has an area of 64 square meters. What is the lenht of each side
Answer:
8 m
Step-by-step explanation:
All the sides of a square are equal.
let x = length of one side
A = x² = 64 m²
√x² = x = √64 = 8
For the function f, f (0) = 86, and for each increase in x by 1, the value of f (x) decreases by 80%. What is the value of f (2)?
Answer:
55
Step-by-step explanation:
80% ^ 2 = 0.64
so f(2) = 86*0.64 = 55
how far away is the puddle from the house? angle of depression is 40 degree
Answer: 29.8 feet
Step-by-step explanation:
To solve this, the first step is to make the imaginary triangle (look at the picture below). Now, we use the basic trigonometry functions. Since we have to find tge base part of the triangle (which is the adjacent one to the angle, and we already have the opposite to the angle. So, now we know we have to use the tan ratio. We now solve it with the following method:
[tex]tan(Angle) = \frac{Opposite}{Adjacent} \\[/tex]
Now we sub in our values and use the calculator to solve it:
[tex]tan(40) = \frac{25}{x}\\\\x = \frac{25}{tan(40)} \\\\x = 29.8 (1 d.p)[/tex]