The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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Consider function f. f(x)=square x-1 which graph represents f?
The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:
C. Graph Y.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.
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BIL
K-7 ft-X-8 ft-
K
-20 ft-
✈
The simplified expression of K-7 ft-X-8 ft-K-20 ft is -35ft-X
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is K-7 ft-X-8 ft-K-20 ft
We need to simplify the given expression.
Add the like terms
-7 ft-X-8 ft-20 ft
-27ft-X-8 ft
-35ft-X
Hence, -35ft-X is the simplified expression of K-7 ft-X-8 ft-K-20 ft
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A, B, C and D are four towns.
B is 40 kilometres due East of A.
C is 40 kilometres due North of A.
D is 65 kilometres due South of A.
a) Work out the bearing of B from C.
135
b) Calculate the bearing of D from B.
Answer
+
G
a) The bearing of B from C is; 45° South-East.
b) The bearing of D from B is; 58.39° South Of West
How to calculate the bearing?a) Distance Between B and C is;
BC = √( 40² + 40²)
= 40√2
= 56.57 km
Angle of B from C = Tan⁻¹( 40/40) = 45°
Bearing of B From C = 45° South Of East
Or 90 - 45° = 45°
45° East of South
Thus, that is the bearing of B from C
b) Distance Between B and D is;
BD = √(40² + 65²)
= 76.32 km
Angle of D from B = Tan⁻¹( 65/40)
= 58.39 °
Bearing of D From B = 58.39° South Of West
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The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answer:
3 lunch specials are possible.
I need the modulus of: I 9+40i I
I = absolute value
The required modulus is 41 .
Complex Numbers:A real and imaginary number combo with the formula a + bi , where
a and b are real numbers, and
i is the "unit imaginary number" √(−1)
a and b may also have zero values.
We are aware that complex numbers are made up of both actual and fictitious numbers.
The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.
Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]
Here, 9 and 40 are substituted for x and y.
i.e. 9+40i
We square the coefficients, add them, and then find the square root to obtain the modulus.
|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]
By long division method we find that
|9+40i| =41
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The ratio of first- class, second- class and third-class passengers who survived the ship wreak is
101:59:89. How many passengers were saved if the total number of first-class passengers were 202?
Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.
If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.
Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.
Step-by-step explanation:
Multiply
-1/5. (-2/7)
Write answer in simplest form.
Answer:
2/35
Step-by-step explanation:
[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]
Devaughn is 8 years older than Sydney. The sum of their ages is 94. What is Sydney's age?
Answer:
Step-by-step explanation:
S+8=D
S+D equals 94.
94/2= 45+2=47
47-8=39
Sydney is 39
Answer:
43
Step-by-step explanation:
94-8= 86
86/2= 43
43+8= 51
a:43
prove it :
51+43= 94
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
After 1 day, each woman would have made 8 scarves.
How many scarves would each woman have made?The expression that represents the number of scarves that Greta can make each day is:
Number of scarves she can make = number of scarves already made + (number of scarves she can make per day x number of days)
= 7 + d
The expression that represents the number of scarves that Evelyn can make each day is:
Number of days x number of scarves she can make per day
d x 8 = 8d
When both of them make the same number of scarves, the two expressions above would be equal.
7 + d = 8d
7 = 8d - d
7 = 7d
d = 7/7
d = 1 day
Number of scarves that would be made in 1 day = 8 x 1 = 8 scarves
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-5,4)A(−5,4), B(4,4)B(4,4), C(4,1)C(4,1), D(1,1)D(1,1), E(4,-3)E(4,−3), F(4,-6)F(4,−6), G(-5, -6)G(−5,−6)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Divide the figure is into two rectangles and a triangle.
The points B, C, E, and F form a rectangle with base BC and height 7 units.
The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.
The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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find the sum of the series. make sure you use the formula and show your work for credit.
please help me I didn't get this at all!
Answer:
The sum of the series is 260.
------------------------
Each term of given series is expressed as:
tₙ = 3n - 1This is an arithmetic progression with 13 terms and the first and last terms are:
t₁ = 3*1 - 1 = 2t₁₃ = 3*13 - 1 = 38Use the sum of the first terms of AP formula:
Sₙ = (t₁ + tₙ)*n/2S₁₃ = (2 + 38)*13/2 = 40*13/2 = 20*13 = 260Answer:
The sum of the series is 260.
Step-by-step explanation:
[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]
The given sigma notation means:
Sum of the series with nth term (3n - 1), starting with n = 1 and ending with n = 13.As (3n - 1) is linear, the series is arithmetic.
The first term (n = 1) is:
a₁ = 3(1) - 1 = 2The second term (n = 2) is:
a₂ = 3(2) - 1 = 5The third term (n = 3) is:
a₃ = 3(3) - 1 = 8… and the last term (n = 13) is:
a₁₃ = 3(13) - 1 = 38Therefore, we need to find 2 + 5 + 8 + ... + 38.
Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.
[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]
Therefore, the sum of the series is 260.
Which of the following expressions is equivalent to the logarithmic expression below? log4 7/x^3
Answer:
D
Step-by-step explanation:
using the rules of logarithms
• log a - log b = log ([tex]\frac{a}{b}[/tex] )
• log [tex]x^{n}[/tex] = nlog x
then
[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]
= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³
= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x
Find the value of X , Y, and z in the parallelogram below.
Answer:
[tex]x = -64\\\\y = -63\\\\z = -57[/tex]
Step-by-step explanation:
Diagonally opposite angles of a parallelogram are equal
Therefore
-y - 3 = 60
Add 3 to both sides; -3 terms on left side cancel out
- y = 60 + 3
- y = 63
Multiply both sides by -1
-1(-y) = -1(63)
y = - 63
Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.
Rephrased,
The consecutive or adjacent angles are supplementary which means they add up to 180°
We see that -2z + 6 and 60° are adjacent angles
So
- 2z + 6 + 60 = 180
-2z + 66 = 180
-2z = 180 - 66
-2z = 114
z = 114/-2
z = -57
Similarly
-2x - 8 + 60 = 180
-2x + 52 = 180
-2x = 180 - 52
-2x = 128
x = 128/-2
x = -64
The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle?.
The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.
The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.
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The number of a country's unemployed workers increased from 3.4 million to 5.5 million last year. If the country's population remained constant at 76 million, how did its unemployment rate change last year? A. It increased by about 27%. B. It decreased by about 27%. C. It increased by about 3%. D. It decreased by about 3%.
The rate at which its unemployment changes is, 54.6 %
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
Given that,
The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.
The change in the number of unemployed workers is:
5.5 million - 3.4 million = 2.1 million
To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:
76 million - 3.4 million = 72.6 million
Now, we can calculate the initial unemployment rate as:
3.4 million / 72.6 million = 0.0469 or 4.69%
Similarly, the final unemployment rate is:
5.5 million / 76 million = 0.0724 or 7.24%
The change in the unemployment rate is:
(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%
Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.
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Find the magnitude of the sum
of these two vectors:
The magnitude of the sum of these two vectors is 2.9486m
What is cosine rule?In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.
The parameters that will help us to find the magnitude are
/OB/ = 3.14m
/OA/ = 2.71 m
Let /AB/= x
Sum of the angles is (-60+30)⁰ = 30⁰
Using cosine rule
x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰
x² = 9.8596+7.3441 -8.5094
x²= 17.2037 -8.5094
x²= 8.6943
x = √8.6943
x = 2.9486
Therefore, the magnitude of the sum
of these two vectors is 2.9486m or 2.9m approximately
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Kylie has 6 boxes. Each box contains 4 cakes. Kylie writes a calculation to find out how many cakes she has in tota 6×4 (a) Write a different way to calculate the total number of cakes. You must not use multiplication.
Answer:
Step-by-step explanation:
6x4=24
another way of writing it is using addition
add 4, six times
so
4+4+4+4+4+4
6 boxes each has four cakes
Help with question 12 (a & b):
A beginning employee will produce 3 items per day
An experienced employee will produce 17 items per day
The number of items per dayBeginning employee
From the question, we have the following parameters that can be used in our computation:
[tex]P\left(d\right)=3\ +\ 15\left(1-e^{-0.2d}\right)[/tex]
Next, we plot the graph (see attachment)
A beginner employee is represented as d = 0
From the graph, we have
P(0) = 3
An experienced employee
Using the graph as a guide, we have
The maximum number of production approximates to 17
This represents the number of items per day for an experienced employee
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The confidence interval for a population proportion is (0.61, 0.81). What the the sample proportion and the margin of error.
The margin of error for the confidence interval for a population is 0.71 ± 0.1.
What is margin of error?The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.
The margin of error is given as:
MOE = U - L / 2
MOE = 0.81 - 0.61 / 2
MOE = 0.2 / 2
MOE = 0.1
The interval is:
Interval = P ± 0.1
Interval = (0.61 + 0.1) ± 0.1
Interval = 0.71 ± 0.1
Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.
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(Combinatorial analysis question)
A batch of 15 phones contains 3 defective phones. A sample of 4 phones out of 15 in the lot is chosen at random. How many of the possible samples contain at least one defective part?
Book says the answer is 870. Can someone give me a step by step answer please?
Answer:
Step-by-step explanation:
There are several ways to approach this problem, but one common method is to use the complementary counting principle, which states that the number of favorable outcomes can be obtained by subtracting the number of unfavorable outcomes from the total number of outcomes. In this case, the favorable outcome is that the sample contains at least one defective phone, and the unfavorable outcome is that the sample contains no defective phones.
The number of possible samples of 4 phones out of 15 can be calculated as the number of combinations of 4 items from a set of 15, which can be written as:
C(15, 4) = 15! / (4! * (15 - 4)!) = 1365
The number of samples containing no defective phones can be calculated as the number of combinations of 4 phones out of the remaining 12 non-defective phones, which can be written as:
C(12, 4) = 12! / (4! * (12 - 4)!) = 495
So, the number of samples containing at least one defective phone can be calculated as:
1365 - 495 = 870
Therefore, out of the 1365 possible samples of 4 phones, 870 of them contain at least one defective phone.
ons
Write the equation for this relationship and identify the constant of proportionality (or k value).
X
Y
28 36 40
21
27
30
56
42
12x + 7 < −11
OR
5x-8>40
Answer:
x <-1.5
or
x <9.6
Step-by-step explanation:
12x + 7 < - 11
12x < -11 - 7
12x < - 18
12x/12 < -18/12
x = -1.5
OR.
5x - 8 > 40
5x > 40 + 8
5x > 48
5x/5 > 48/5
x > 9.6.
Find the value of x.
(4x+12) 64°
OA. 19
OB. 3.5
O c. 26
OD. 13
Answer: OD. 13
Step-by-step explanation:
Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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In complete sentences, explain how to determine the angle measurement for this angle.
WRITER
28
90
50
40 50 60 70
140 130 120 110
£10
umumla
150
30 20 10
160 170 180
UPLOAT
(2
The procedure for angle measurement by the protractor is mentioned below:
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
To measure an angle using a protractor, follow these steps:
1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.
2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.
3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.
If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.
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NEED HELPP!!!!!!!!!!!!
Answer:
the last one
Step-by-step explanation:
first you have to distribute the 5 to all the variables.
when you do that you get
x---9x5=45
y---1x5=5
z---4x5=20
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The length of a rectangle is 6 feet less than 4 times the width. If the perimeter is 68 feet, find the length and the width of the rectangle.
Answer:
Length = 26 feet; Width = 8 feet
Step-by-step explanation:
Let:
x = Length of rectangle
y = Width of rectangle
4 times the width = 4y
∴ 6 less than 4 times the width = 4y - 6
Perimeter of a rectangle = 2 × [Length + Width]
68 = 2 × [(4y - 6) + y]
Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:
68 = 2 × [4y - 6 + y]
68 = 2 × [5y - 6]
68 = 10y - 12
68 + 12 = 10y
Isolate y by making it the subject of the equation:
80 = 10y
y = [tex]\frac{80}{10}[/tex]
y = Width of rectangle: 8 feet
Substitute y into the equation to calculate x:
x = 4(8) - 6
x = Length of rectangle = [tex](32 - 6)[/tex] feet
x = 26 feet
Given the letters H A M I L T O N in a game of scrabble:
a) How many ways can you arrange all of the letters if the arrangement must end in a vowel [vowel: a,e,i,o,u]
b) How many arrangements are there if you can only use five letters?
The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.
The number of arrangement using only five letters is; 6720.
What is the number of ways to arrange the letters as described?Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.
Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!
= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.
b). The number of arrangements if one can only use five letters is; ⁸P₅
= 6720.
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Suppose f(x)= 10x-4
Compute the following:
A.) f(x-2)+f(2x)
A.) f(x-2)+f(2x)
To find this expression, we can substitute the definition of f(x) into the expression and simplify:
f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]
= 10x - 20 - 4 + 20x - 4
= 30x - 28
Therefore, f(x-2)+f(2x) = 30x - 28.
Compute f(2a) - f(a) for any value of a ?Given f(x) = 10x - 4, we need to find f(2a) - f(a).
f(2a) = 10(2a) - 4 = 20a - 4
f(a) = 10a - 4
Therefore,
f(2a) - f(a) = (20a - 4) - (10a - 4)
= 10a
Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.
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You deposit $9000 in an account earning 5% interest compounded continuously. The amount of money in the account after t years is given by A(t)=9000e^0.05t
How much will you have in the account in 14 years? $ Round your answer to 2 decimal places.
How long will you have in the account in 14 years? ______years. Round your answer to 2 decimals
How long does it take for the money in the account to double? ____ years. Round your answer to 2 decimal places
The amount of money which would be in the account after 14 years is; $18,123.77.
The number of years it'd take for the money to double is; 13.86 years.
What is the doubling time of the compound interest arrangement?Since the given model of the account is;
A (t) = 9000e^0.05t
After 14 years, it follows that; t = 14.
Therefore;
A (14) = 9000e^0.05(14)
A (14) = 9000 × 2.013752707
A (14) = $18,123.77.
Also, the doubling time implies that; A (t) = 18,000
Therefore, 18000 = 9000e^0.05t
2 = e^0.05t
0.05t = ln (2)
t = ln (2) / 0.05
t = 13.86 years.
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