Answer:
£13,110.49
Step-by-step explanation:
(A) = P( 1 + r/n) ^nt
P(Principal) = £200 000
r(interest rate) = 1.6% = 0.016
The total amount been saved after 4 years is calculated as:
A = P( 1 + r/n) ^ nt
A = £200,000( 1 + 0.016/1)¹× ⁴
A = £200,000(1.016)⁴
A = £213,110.48991
A = £ 213,110.49
Claire will get approximately £ 213,110.49 within 4 years.
Exercise Sophia pays a $19.99 membership fee for an online music store. a. If she also buys two songs from a new album at a price of $0.99 each, what is the total cost? b. If Sophia purchases 푛 songs for $0.99 each, write an expression for the total cost. c. Sophia’s friend has saved $118 but is not sure how many songs she can afford if she buys the membership and some songs. Use the expression in part (b) to write an equation that can be used to determine how many songs Sophia’s friend can buy. d. Using the equation written in part (c), can Sophia’s friend buy 101, 100, or 99 songs? Relevant Vocabulary VARIABLE (DESCRIPTION): A variable is a symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number). EQUATION: An equation is a statement of equality between two expressions. NUMBER SENTENCE: A number sentence is a statement of equality between two numerical expressions. SOLUTION: A solution to an equation with one variable is a number that, when substituted for the variable in both expressions, makes the equation a true number sentence.
.
What's the answer for all of them??
Answer:
first, how much were her songs? It's two songs each, and their separate prize was 0.99:
total prize was 2*0.99=1.98
this gets added to the membership prize:
19.99+1.98=21.97
you can also calculate this by rounding all the numbers (20+1+1) and substracting the amount you rounded (three times one cent) - the result would be the same.
B 19.99+.99n
C okay so it says Sophia's friend has saved $118 so she already knows she has $118 and then the next step is to figure out about Part B so she does not know how many songs you can afford to buy so the expression in Part B whatever the expression is if you figured out the answer to Part B and there's a number what you want to do what you would want to divide that number into 118 to see how how many equal groups you can make and you don't want to go overboard 18 so what you would want to do it if you would want to do if you figure out the number to expression be in the boring part B they don't want to take that and keep making a go go to that until you reach 118 and then you would get your total
D N=99 songs
I will give brainliest if you answer please
Answer:
KN = 11
Step-by-step explanation:
In right triangle LNM, by Pythagoras theorem:
[tex]LN=\sqrt{LM^2 -MN^2} \\ \\ \implies \: LN=\sqrt{ {(100)}^{2} -(80)^2} \\ \\ \implies \: LN=\sqrt{ 10000 -6400} \\ \\ \implies \: LN=\sqrt{ 3600} \\ \\ \implies \: LN=60[/tex]
In right triangle LNK, by Pythagoras theorem:
[tex]KN = \sqrt{LK^2-LN^2}[/tex]
[tex]\implies KN = \sqrt{(61)^2-(60)^2}[/tex]
[tex]\implies KN = \sqrt{3721-3600}[/tex]
[tex]\implies KN = \sqrt{121}[/tex]
[tex]\implies\huge{\orange{ KN =11}}[/tex]
Answer:
11[tex] \: [/tex]
Step-by-step explanation:
Before, Finding the length of KN, we must have to find the length of LN. So
[tex] \: [/tex]
Here, LNM is a right angled triangle where measure of two sides are given and we are to find the measure of the third side LN(Perpendicular).
[tex] \: [/tex]
We'll find the measure of third side with the help of the Pythagorean theorem.
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]
Here,
The base (NM) is 80The perpendicular is LNThe hypotenuse (LM) is 100.[tex] \: [/tex]
So, substituting the values in the above formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (NM) {}^{2} + (LN {)}^{2} = ( LM{)}^{2} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (80) {}^{2} + (LN {)}^{2} = ( 100{)}^{2} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = ( 100{)}^{2} - (80) {}^{2}}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 10000 - 6400}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 3600}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad LN = \sqrt{3600} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad LN = \frak{60}}}} \\ \\[/tex]
Therefore,
The length of LN is 60.[tex] \\ [/tex]
As, we found the length of LN, now we can find the length of KN.
Where,
The base is KNThe perpendicular (LN) is 60.The hypotenuse (LK) is 61.So, in the right angled triangle LKN, by Pythagorean theorem we get,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + (LN {)}^{2} = ( LK{)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + {60}^{2} = ( 61{)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = ( 61{)}^{2} - {(60)}^{2}}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} =3721 - 3600}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = 121}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad KN = \sqrt{121} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad KN = \frak{11} }}} \\ \\[/tex]
Therefore,
The length of KN is 11.A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number greater than 10?
Write your answer as a fraction in the simplest form.
Answer:
Here;
Step-by-step explanation:
The numbers greater than 10 are 11 and 12 on the dice meaning we've got 2 options out of 12.
So, 2/12 gives 1/6 in its simplest form
If three numbers 36,54 and another number have a G.C.D of 6 and L.C.M of 216, find the other number
Answer:
24
Step-by-step explanation:
The GCD of a set of numbers is the product of the prime factors, each to the lowest of the powers it has as a factor of any of the numbers.
The LCM of a set of numbers is the product of the prime factors, each to the highest of the powers it has as a factor of any of the numbers.
__
The factorizations of the given numbers are ...
36 = 2^2 × 3^2
54 = 2 × 3^3
__
6 = 2 × 3 . . . . . . . . . . . GCD
216 = 2^3 × 3^3 . . . . . LCM
This tells us the lowest powers of 2 and 3 are 2^1 and 3^1, and the highest powers of 2 and 3 are 2^3 and 3^3. Already, the lowest power of 2 matches the GCD, and the highest power of 3 matches the LCM. What we need is a number with a power of 2 that is 3, and a power of 3 that is 1:
2^3 × 3^1 = 24
The other number is 24.
the ratio of boys to girls in mrs.cunnginghams class is 2 to 3. there are 18 girls in the class. what is the total number of students in mrs.cunninhams class
Answer:
The total number of students that are in Ms. Cunningham's class is 30 students
Step-by-step explanation:
the number of boys are represented by X
18 divided by 3 is 6
2 times 6 is 12.
12 plus 18 is 30.
Total number of students = 12 + 18 = 30
i need help can someone help
Answer:
Step-by-step explanation:
The distributive property is for example 3(2*4) the outside number multiplies everything inside the parenthesis. For the communitive, its like opposites, but they give the same answer, for example 4*5, 5*4. And for associative is like the distributive property, but not at the same time, for example, (a*b)*c = a*(b*c) it has the numbers, but pluged in in another type of way
Hope this helps!
1. the height of a right triangular prism is inches. each side of the triangular base measures 10 inches, and the height of the base is inches. the triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube. what is the surface area of the solid formed?
The surface area of the solid formed by the triangular prism and cube will be 598.33 square inches.
What is a prism?A prism is a closed solid that has two parallel bases connected by a rectangle surface.
The height of a right triangular prism is 11/6 inches.
Each side of the triangular base measures 10 inches, and the height of the base is 26/3 inches.
The triangular prism is placed at top of a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
Then the surface area of the prism will be
[tex]\rm Surface \ area = 5 \times (10 \times 10) + 0.5 \times 10 \times \dfrac{26}{3} + 3 \times 10 \times \dfrac{11}{6}\\\\\\Surface \ area = 598.33\ in^2[/tex]
More about the prism link is given below.
https://brainly.com/question/12649592
Given m|n, find the value of x.
Rt
(6x+9)
(4x-19)
11
Answer:
x = 19
Step-by-step explanation:
See attched image.
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Answer:
please see photo for detailed analysis
Apply properties of operations to show why 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n)
Applying the properties of operations; it follows that; 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n).
Properties of OperationsThere are four (4) basic properties of real numbers which apply to addition and multiplication: namely; commutative, associative, distributive and identity.
Hence, by the cumutative property of multiplication and associative property of addition, it follows that;
4× -1.5 = -21(2/7)3.5n + 4(5 1/4n) = -21(7/6n)Hence, it follows that the expressions are equivalent.
Read more on properties of operations;
https://brainly.com/question/16136176
Find the area of the shaded region. Round to the nearest hundredth where necessary (2 decimal places
A=(
6 in
1
14 in
26 in
15 in
Answer:
117 in²
Finding the area of the trapezoid:
First, we need to find the area of the trapezoid formed by the dotted lines. The formula for finding the area of the trapezoid is "(a₁ + a₂)h/2".
[Where, a₁ = shorter parallel side; a₂ = longer parallel side]
⇒ (a₁ + a₂)h/2 = Area of trapezoid
⇒ (14 + 26)15/2 = Area of trapezoid
⇒ Area of trapezoid = (40)15/2 = (20)15 = 300 in²
Reviewing on how to find the area of the unshaded region:
To find the area of the shaded region, we need to subtract the area of the unshaded region from the area of the trapezoid. In this case, the unshaded region is a triangle whose base is 26 inches. To find the area of the triangle, we need to use the formula 1/2 x Base x Height. We are given the base, but the height is unknown.
Determining the height:
We are given a small side length "6 inches" and the height of the trapezoid "15 inches". If we subtract the small side length from the height of the trapezoid, we will obtain the height of the triangle.
⇒ Height of trapezoid - Small side length = Height of triangle
⇒ 15 - 6 = Height of triangle
⇒ 9 in = Height of triangle
Determining the area of the unshaded region:
Now, let's substitute the base and the height in the formula to find the area of the triangle
⇒ 1/2 x Base x Height
⇒ 1/2 x 26 x 9
⇒ 13 x 9
⇒ 117 in²
Determining the area of the shaded region:
Finally, let's subtract the area of the unshaded region from the area of the trapezoid to obtain the area of the shaded region.
⇒ Area of trapezoid - Area of unshaded region = Area of shaded region
⇒ 300 - 117 = Area of shaded region
⇒ 183 in² = Area of shaded region
Which expression is equivalent to [tex]sin\frac{7\pi }{6}[/tex]?
Check the picture below.
notice, the pairs in the Unit Circle are the (cosine , sine) pair, which are equivalent to (x , y) values in a cartesian plane.
Answer:
D on edg 2022
Step-by-step explanation:
5. A population has a normal distribution with a mean of 50 and a standard deviation of
10. If a random sample of size 9 is taken from the population, then what is the
probability that this sample mean will be between 48 and 54?
a. 0.060
b. 0.228
c. 0.385
d. 0.399
e. 0.611
Using the normal distribution and the central limit theorem, it is found that the probability is given by:
e. 0.611
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 50, \sigma = 10, n = 9, s = \frac{10}{\sqrt{9}} = 3.3333[/tex]
The probability that this sample mean will be between 48 and 54 is the p-value of Z when X = 54 subtracted by the p-value of Z when X = 48, hence:
X = 54:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{54 - 50}{3.3333}[/tex]
Z = 1.2
Z = 1.2 has a p-value of 0.885.
X = 48:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48 - 50}{3.3333}[/tex]
Z = -0.6
Z = -0.6 has a p-value of 0.274.
0.885 - 0.274 = 0.611, hence option e is correct.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
Can someone help me with this pls
Correct solution:
⇒ 8 ÷ 1/8⇒ 8 x 8⇒ 64Find the missing angle
Step-by-step explanation:
a + 156° = 180° ( supplementary angle )
a = 180° - 156°
a = 24°
I NEED HELP FAST
I will mark brainliest whoever gets it right
its b i know
Step-by-step explanation:
The hypotenuse of a right triangle measures 6cm and one of its legs measures 3cm.Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
5.2
Step-by-step explanation:
a^2+b^2=c^2
Where c is the length of hypotenuse
and a, b are lengths of the legs.
Put in 6 for c,
Put in 3 for a and you get 9+b^2=36
Subtract 9 from both sides and get b^2= 27
Then find the square root of both sides to get b, so the answer is the square root of 27.
The cloest square root is 5, then apporixmate the tenths value and see if they work.
Answer: 5.2
Answer:
square root of 27, 5.2
Step-by-step explanation:
(I know I'm late but-)
3^2+b^2=6^2
9+b^2=36
b^2=27
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answer:
third side: 2√14
using pythagoras theorem:
a² + b² = c²
t² + 5² = 9²t² + 25 = 81t² = 81 - 25t² = 56t = √56t = 2√14Answer:
The unknown side of this triangle is √56 or 2√14
Step-by-step explanation:
Let the unknown side of this right angled triangle be x , so by using Pythagoras theorem we can find out the third side .
=> P² + B² = H²
=> P² = H² - B²
=> P² = 9² - 5²
=> P² = 81 - 25
=> P² = 56
=> P = √56 or 2√14
The Molina family's pancake recipe uses 2 teaspoons of baking powder for every 1 3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
Answer: 7
Step-by-step explanation:
2q^2+5+2q+–3+10+–5q
how do I do this?
Answer:
First you add up all the numbers and then the unknowns.
Step-by-step explanation:
2q^2+12-2q-5q
2q^2+12-3q
2q^2-3q+12
Jon is taking a 625 mile trip. On the first day, he drove 183 miles.
How many more miles does he have to drive?
part b
Type and solve an equation to find how many more miles Jon has left to drive.
part A Verify your solution.
Part A: Jon has 442 miles left to drive.
ex: 625 - 183 = 442
An auditorium has rows of seats with a seats in each row Kayla
knows there are at least 70 seats but fewer than 156 seats in the
auditorium. How many rows of seats can there be in the auditorium
Use Exercises 1-a to answer the question
1. Explain how you would find the least possible number of rowe
in the auditorium
2. How would you find all the possible numbers of rows, without
having to check if & is a factor of every number between
70 and 1507
3. Name all the possible numbers of rows in the auditorium,
Step-by-step explanation:
Note: there is a typo, 'a' should be '8'The number of seats in each row is 8 and the total number of seats is between 70 and 150.
Let x be the number of rows, then we have the inequality:
70 ≤ 8x < 156Divide all sides by 8 to get:
70/8 ≤ x < 156/89 ≤ x ≤ 19 (taking closest integers)So the number of rows is between 9 and 19 both inclusive.
All possible number of rows
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19Answer:
1. 9 rows
2. see below
3. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Step-by-step explanation:
Please note that I believe there are typing errors in the question and that the given information should be:
8 seats in each rowAt least 70 seatsLess than 150 seatsQuestion 1
To determine the least possible number of rows in the auditorium, divide the least number of seats by the number of seats in a row:
⇒ 70 ÷ 8 = 8.75
As the answer is a decimal, round it up to the nearest whole number.
Therefore, the least possible number of rows in the auditorium is 9 rows.
Question 2
Find the greatest number of rows by dividing the greatest number of seats by the number of seats in a row:
⇒ 150 ÷ 8 = 18.75
As there should be fewer than 150 seats we cannot round the number up (as this would make there be more than 150 seats), so instead must round it down to 18.
Therefore, the greatest number of rows in the auditorium is 18 rows.
Question 3
As we have found the least number of rows in question 1 and the greatest number of rows in question 2, all we need to do is list all the numbers between (and including) these numbers.
Therefore, all the possible numbers of rows in the auditorium are:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Please help me this is hard and its due today!
Answer: A, C and E.
Step-by-step explanation: They all equal to 5.
Kate has a coin collection. She keeps 7 in a box, which is only 5% of her entire collection. What is the total number of coins in Kate’s coin collection?
Answer:
140
Step-by-step explanation:
5%/100 = 7/?
7 times 100 = 700
700 divided by 5 = 140 coins
A map uses a scale of centimeter 0.5 = 75 kilometers. The actual distances between various cities are are at 40 kilometers
4. Sebastian's lemonade recipe uses 4 cups
of water and 1 cup of lemon concentrate.
What is the percentage of the lemonade
recipe that is lemon concentrate,
Please help me I really need it
Answer: 170
Step-by-step explanation: Like I answered before: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.
Answer:
<CDA = 170⁰
Step-by-step explanation:
<A + <D = 180⁰ { Adjacent Angles of an parallelogram are supplementary}
10⁰ + <D = 180⁰
<D = 180⁰ - 10⁰ = 170⁰
<D = x⁰ = 170⁰ = <CDA
If the point with coordinate
(k,7) lies on the equation 2x−y=5 determine the value of k
Answer:
k = 6
Step-by-step explanation:
since (k, 7 ) lies on the line then it satisfies the equation.
substitute the coordinates of the point into the equation and solve for k
2k - 7 = 5 ( add 7 to both sides )
2k = 12 ( divide both sides by 2 )
k = 6
Answer:
k = 6
Step-by-step explanation:
The point (k, 7) lies on the line with the equation 2x - y = 5
Substitute the coordinates of the point in the equation2(k) - 7 = 52k = 12k = 6What is the measure of \angle R∠Rangle, R?
Answer:
106⁰
Step-by-step explanation:
As in cyclic quadrilateral sum of opposite angles is equal to 180⁰
Use the point-slope form of a line to write the equation of
a line that has a slope of 2 and passes through the point
(4,3). Write the equation in slope-intercept form.
Answer:
y=2x-5
Step-by-step explanation:
Hi there!
We are given that a line has a slope of 2, and passes through the point (4,3)
We want to use point-slope form to find this equation of the line, yet we want to write this in slope-intercept form
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
As we are already given the slope and a point, we can substitute these values into the formula to find the line.
First, substitute 2 as m in the equation:
[tex]y-y_1=2(x-x_1)[/tex]
Now substitute 4 as [tex]x_1[/tex] and 3 as [tex]y_1[/tex]
[tex]y-3=2(x-4)[/tex]
This is the equation of the line in point-slope form.
Now we need to write it in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
We can actually get to slope-intercept form from point-slope form.
First, distribute 2 to both x and -4 on the right side
y-3=2x-8
Now add 3 to both sides
y=2x-5
Hope this helps!