As per the given percentage, the value of the loan 10 years after it starts is £4506.32.
We know the values of P and A for the first two years. So, we can use these values to find the value of r. Let's use the formula for the first year:
2645 = 2500(1 + r/1)¹ˣ¹
Simplifying the equation, we get:
1 + r = 2645/2500
1 + r = 1.058
r = 0.058 or 5.8%
Therefore, the interest rate per annum is 5.8% (to 1 decimal place).
Now, let's move on to finding the value of the loan after 10 years. We can use the same formula for compound interest, but we need to substitute the values of P, r, n, and t accordingly. Here's the formula:
A = P(1 + r/n)ⁿˣ
Where:
P = 2500
r = 0.058
n = 1 (as the interest is compounded annually)
x = 10
Substituting these values, we get:
A = 2500(1 + 0.058/1)¹ˣ¹⁰
A = 2500(1.058)¹⁰
A = 4506.32
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Given that NL HI and NM JK, find the radius of circle N if JK=14. Round the answer to the hundredths place. A. 12.56 B. 12.57 C. 13.03 D. 13.04
The value of the radius is 13.04
What is Pythagoras theorem?Pythagoras theorem states that: The sum of square of the two legs of a right triangle is equal to the square of the other side.
Therefore c² = a² + b²
Since MN is perpendicular to JK , this means MK = JM = JK/2
= 14/2 = 7
HI = JK, therefore LI is also 7
and MN = LN = 11
Therefore,
NI =√ LN)² + LI)²
NI = √ 11² + 7²
NI = √121+49
NI = √ 170
NI = 13.04( nearest hundredth)
therefore the radius of the circle is 13.04
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What function is represented in the graph?
Select one:
y = 2(.5^x)
y = 2(3^x)
y = 3(.5^x)
y = 3(2^x)
The exponential function represented by the given graph is:
y = 2(.5^x)
What function is represented by the graph?Here we have an exponential decay, the general form of these functions is:
y = A*(b)^x
Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.
Now let's look at the y-intercept, we can see that it is y = 2, then:
2 = A*(b)^0
2 = A
The function is of the form:
y = 2*(b)^x with 0 < b < 1.
The option that meets these conditions is the first one: y = 2(.5^x)
So that is the correct option.
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plot a point to represent the approximation sqrt(20)
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
|---------------------|---------------------|
0 4.472
We have,
To plot the point representing the approximation of √(20), we need to first find the approximate value of √(20):
√(20) ≈ 4.472
This means that the point we want to plot is located approximately 4.472 units to the right of the origin on the number line.
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
The resulting point represents the approximation of √(20).
Thus,
A rough sketch of what the plot could look like:
|---------------------|---------------------|
0 4.472
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Josh weighed cantaloupes he picked from his garden. This line plot shows the cantaloupe weights. What is the total weight of all the cantaloupes that weigh more than 2 1/2 pounds?
7 3/4 lb
8 lb
8 1/4 lb
8 2/4 lb
The total weight of all the cantaloupes that weigh more than 2 1 / 2 pounds is 8 2 / 4 lb .
What is the total weight ?As shown on the line plot, the number of cantaloupes with a higher mass than 2 1 / 2 pounds are those which have a weight of 2 3 / 4 pounds.
There are enough of them that when they are added up, we get the sum of 8 2 / 4 lb as the total mass of the cantaloupes. This can also be written in decimals as 8. 5 lb.
In conclusion, option D. is correct.
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A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made
from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)
Answer:
499,237 ft²
Step-by-step explanation:
You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.
AreaTo find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:
A = 1/2bh
There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:
4A = 4(1/2bh) = 2bh
Slant heightThe slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)
h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet
Glass arealateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²
The surface area of the glass is about 499237 square feet.
A slide at a water park with a constant slope sends riders traveling a distance of 45 feet to the pool at the bottom of the slide. If the depth of the pool is 12 feet, and the angle of depression from the top of the slide is 45 ° what is the vertical distance from the top of the slide to the bottom of the pool? Round answers to the nearest tenth.
The required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
We can use trigonometry to solve this problem. Let's call the vertical distance from the top of the slide to the bottom of the pool "h" (in feet). We can use the angle of depression (45°) to find the horizontal distance from the top of the slide to the bottom of the pool. Since the slide has a constant slope, the angle between the slide and the ground is also 45°. It implies that the vertical height is equal to the horizontal projection of the slide.
Apply Pythagorean theorem,
45² = h² + h²
h = 45/√2
h = 31.8
Now, as mentioned that depth of the pool is 12 feet so, the total vertical height is given as,
= h + 12
= 31.8 + 12
= 43.8 feet
Thus, the required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
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The Winberg apartment complex rents out units at $200x monthly for each of their 9 units. The Hensing apartment complex has 3x more units and rents out each unit for $20 less monthly.
Which of the following equations could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out?
A. y = $(600x^2 - 180)
B. y = $(600x^2)
C. y = $(600x^2 + 1,740x - 180)
D. y = $(600x^2 + 1,860x - 180)
The equation that could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out is A. y = $(600x^2 - 180).
How to calculate the equationThe Hensing apartment complex rents out each unit for $20 less monthly than the Winberg complex, so the rent for each unit is $200x - $20 = $180x.
The equation that represents this situation is: y = $(600x^2 - 180
So the answer is (A) y = $(600x^2 - 180).
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The triangles below are similar. Find the value of X. The image is not to scale
Answer:
x is 25
Step-by-step explanation:
There is a common ratio between the sides. In this case, 35/28 is 1.25. This is the number you have to multiply to 20. 1.25 * 20 = 25.
In a greenhouse, Brazil is grown in planters that have a base of 4 1/5 In by 1 1/3 in. If there is a 3 x 3 array of these planters with no space between them, what is the area covered by the planters
Answer:
The area of one planter is:
4 1/5 in × 1 1/3 in = (21/5) in × (4/3) in = 28/5 in²
In a 3 x 3 array, there are 3 planters in each row and 3 planters in each column, so there are a total of 9 planters.
The area covered by the planters is:
9 × (28/5) in² = 252/5 in² ≈ 50.4 in²
Therefore, the area covered by the planters is approximately 50.4 square inches.
Step-by-step explanation:
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What is angle CAB
Enter your answer in the box
The measure of the angle CAB in a right angled triangle ABC using given measurements is equal to 37°.
In the triangle ABC,
From the figure we have,
Measure of angle ABC = 90 degrees
Measure of angle ACB= 53 degrees
Sum of all the interior angles of a triangle is equal to 180 degrees .
⇒Measure of angle ABC + Measure of angle ACB + Measure of angle CAB = 180 degrees
⇒ 90° + 53° + Measure of angle CAB = 180°
⇒143° + Measure of angle CAB = 180°
⇒ Measure of angle CAB = 180° - 143°
⇒ Measure of angle CAB = 37°
Therefore, the measure of the angle CAB is equal to 37°.
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Which of the following equations describes the
graph below?
Answer:
5x + 3y = - 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line
m = [tex]\frac{-5-0}{0-(-3)}[/tex] = [tex]\frac{-5}{0+3}[/tex] = - [tex]\frac{5}{3}[/tex]
the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5
y = - [tex]\frac{5}{3}[/tex] x - 5 ← in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 5x - 15 ( add 5x to both sides )
5x + 3y = - 15 ← in standard form
A
Select the correct answer.
Which system of linear inequalities is represented by this graphed solution?
OA y> -+2
V≤ 32-1
OB V<= +2
v2 32-1
Ocy> -2x + 2
vs-1
OD S-2 +2
v < 30-1
The two inequalities of the graph are:
y ≥ 3x - 1
y < -¹/₂x + 4
How to identify inequality graph?
The general form of the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.
Two coordinates on the line are: (0, -1) and (1, 2)
The slope = (2 + 1)/(1 - 0) = 3
Thus, inequality is:
y ≥ 3x - 1
The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.
Two coordinates on the line are: (4, 0) and (0, 2)
The slope = (2 - 0)/(0 - 4) = -1/2
Thus, inequality is:
y < -¹/₂x + 4
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3
2
A ABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of
create A A'B'C'.
The center of dilation is the point (5,
(5,
-6).
What are the coordinates of vertex.
B'₂
Enter your answers, as decimals, in the boxes.
9
The coordinates of vertex B' are (76, -86).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate B, we have;
Coordinate B = (4, -4) → (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))
Coordinate B = (4, -4) → (9(9) - 5, 9(-9) - 5)
Coordinate B = (4, -4) → (81 - 5, -81 - 5)
Coordinate B' = (76, -86).
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Complete Question:
ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).
What are the coordinates of vertex B'?
Sarah is building a 10-foot-long pen for her pet rabbits. She wants to make gravel bases for two circular food containers to go inside the pen along with its width, as shown in the diagram. Let y represent the width of the pen and x represent the radii of the gravel bases and food containers. What system of inequalities can be used to determine the width of the pen, y, and the radii of the gravel bases, x?
1. The width of the pen must be greater than or equal to the sum of the diameters of the two circular food containers, which is equal to 2x + 2x = 4x:
y ≥ 4x2. The width of the pen must also be less than or equal to the length of the pen, which is 10 feet:
y ≤ 103. The radii of the gravel bases must be greater than or equal to the radii of the food containers, which is equal to x:
x ≥ x4. The radii of the gravel bases must also be less than or equal to half the width of the pen, which is equal to y/2:
x ≤ y/2SYSTEM OF INEQUALITIESSystem of inequalities that can be used to determine the width of the pen, y, and the radii of the gravel bases, x, is:
y ≥ 4xy ≤ 10x ≥ 0x ≤ y/2Answer:
Step-by-step explanation:
The sum of the diameters of the gravel bases cannot exceed the width of the pen, so 2x+2x≤y. Rewrite this to get y≥4x as the first inequality in the system.Next, to write the expression for the cost of the fencing, find the perimeter of the rectangle and multiply the perimeter by the cost per foot of fencing. The pen is a rectangle, so the perimeter is 2(10)+2(y), or 20+2y. Multiply the cost ($4.00 per foot) by the perimeter to get 4(20+2y).Now write an expression for the gravel bases for the circular food containers. Because A=πr2 and the cost of the gravel is $2.00 per square foot, multiply the cost of the material by the sum of these areas to get 2(πx2)+2(πx2).The total cost must be less than or equal to $150, so we can say that 4(20+2y)+2(πx2)+2(πx2)≤150. Finally, simplify and solve for y.80+8y+2πx2+2πx2≤15080+8y+4πx2≤1508y≤70−4πx2y≤8.75−0.5πx2So, this is the system.
y≥4x
y≤8.75−0.5πx2
A set of data items is normally distributed with a mean of 80 and a standard deviation of 9. Convert 71 to a z-score.
271 = 0
(Type an integer or a decimal.)
The z-score for 71 is -1.
Understanding Z-score calculationz-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.
It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ
A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.
Applying the formula to solve our question
Here is a proven formula to use:
z = (x - μ) / σ
where:
x = the data item (x = 71)
μ = the mean of the distribution (μ = 80)
σ = the standard deviation of the distribution (σ = 9)
Substituting the values, we get:
z = (71 - 80) / 9
z = -1
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find the mean of the set of data 3,5,4,4,5,7,7
Answer:
mean=5
Step-by-step explanation:
To find the mean of a set of data, we add up all the values in the set and then divide by the number of values.
Adding up the values in the set, we get:
3 + 5 + 4 + 4 + 5 + 7 + 7 = 35
There are 7 values in the set, so we divide the sum by 7 to get the mean:
mean = sum of values / number of values
mean = 35 / 7
mean = 5
complete the table on the relation
256 chairs in the cafeteria. this is 8 times as many chairs in the library. total chairs in the library
Answer:
32
Step-by-step explanation:
in the word problem “256 chairs in the cafeteria. this is 8 times the chairs in the library.” Which means 8 times the number of chairs in the library equals the number of chairs in the cafeteria.
L = library
8 x L = 256
to find L divided 256 by 8
256/8 = 32
L = 32
Check the answer
8 x 32 = 256
Find the distance between (-2.1,80°) and (-1.8,-70°)
Answer:
15,136 km
Step-by-step explanation:
Im not 100% sure but everyone meses up sometimes/
(CLASSKICK) HELP ASAPPPP!
The value of the angle 3 as solved is 52 degrees.
What is the sum of the angles on a straight line?
The sum of the angles on a straight line is always 180 degrees, and this property is true for any pair of opposite angles formed by two intersecting lines.
We can see that what we have is the angles that are on a straight line
We have from the question that;
< 1= 90
<2 = 38
Thus;
<6 = 180 - (90 + 38) - Sum of angles on a straight line
<6 = 52°
Now;
<4 = 90 degrees (Vertically opposite angles)
<5 = 38 degrees (Vertically opposite angles)
Then;
<3 = 180 - (90 + 38) - Sum of angles on a straight line
<3 = 52°
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WHATS THE 2ND TO THE POWER OF THE 4TH
Answer:
16.
Step-by-step explanation:
Classifying the polynomial
Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.
solve the proportion for x pls help image attached
[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]
The volume of the tank is cubic feet and it will be completely filled with water at the end of minutes.
Answer:
there is missing information needed to provide a solution to this problem.
lamonte car used 5 gallons to travel 125 miles.how many gallons of gas would he need to travel 400 miles
Answer:
Step-by-step explanation:
1. Get mileage per gallon by dividing miles traveled by gallons used
[tex]\frac{125}{5} = 25 mpg\\[/tex]
2. Divide miles you want to travel by the mileage per gallon you got on the first step
[tex]\frac{400}{25} = 16 gallons[/tex]
Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.
The null hypothesis and the alterative hypothesis are [tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220.
The standardized test statistic is 1.725.
We have,
[tex]\mu[/tex] > 1220,
α = 0.03
[tex]\sigma[/tex] = 202.17
X = 1249.88
n= 300
a) According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:
[tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220
b) The standardized test statistic is
=| [tex](\mu[/tex] - X) / ([tex]\sigma[/tex] / √n)|
= |( 1220 - 1249.88) / (202.17/√300)|
= |(-29.88)/ 17.320|
= |-1.725|
= 1.725
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Solve the equation below. Give the solution as an integer or reduced fraction.
log5 (x-7)= 2
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(x-7)=2\implies 5^{\log_5(x-7)}=5^2\implies x-7=5^2 \\\\\\ x-7=25\implies x=32[/tex]
The boxplot displays the total cost of attendance for all US public and private universities.
Use this graphic to complete the statements.
Both distributions of the total cost of attendance are
. The average cost of attendance is higher for
universities. The costs of more than
% of the public institutions were within the costs of the lowest 25% of private institutions. Both the range and IQR was higher for
universities. Both distributions have
outliers.
Both distributions of the total cost of attendance are skewed right
The average cost of attendance is higher for private universities.
The costs of more than 75 % of the public institutions were within the costs of the lowest 25% of private institutions.
Both the range and IQR was higher for private universities
Both distributions have outliers.
What is a box plot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).
It can tell you about your outliers and what their values are
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Answer:
skewed right private 75 private do have outliers
Step-by-step explanation:
Zeke and his stepmother wanted to start volunteering together. They found 9 opportunities online, 7 of which involved working at an animal shelter.
If they randomly chose to apply to 6 of the opportunities, what is the probability that all of them involve working at an animal shelter?
The likelihood that they will choose to work in an animal shelter for each of the six options they choose is around 0.2214 or 22.14%
The probability is given as,
P = (Favorable event) / (Total event)
The likelihood of choosing an opportunity at an animal shelter is 7/9. If each chance is equally likely to be chosen, the likelihood of choosing six in a row from an animal shelter may be estimated by multiplying the likelihood of choosing one opportunity by itself six times:
P = (7/9) x (7/9) x (7/9) x (7/9)
P = (7/9)⁶
P = 0.2214 or 22.14%
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Simplify to an expression involving a single trigonometric function with no fractions.
[tex]\sin^2(\theta)+\cos^2(\theta)=1\hspace{9em} \begin{array}{llll} \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \\\\ \cos(-\theta )=\cos(\theta ) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cot(-x)\cos(-x)+\sin(-x)\implies \cfrac{\cos(-x)}{\sin(-x)}\cos(-x)+\sin(-x) \\\\\\ \cfrac{\cos(x)}{-\sin(x)}\cos(x)+[-\sin(x)]\implies \cfrac{-\cos^2(x)}{\sin(x)}-\sin(x) \\\\\\ \cfrac{-\cos^2(x)-\sin^2(x)}{\sin(x)}\implies \cfrac{-( ~~ \cos^2(x)+\sin^2(x) ~~ )}{\sin(x)} \\\\\\ \cfrac{-( ~~ 1 ~~ )}{\sin(x)}\implies -\cfrac{1}{\sin(x)}\implies -\csc(x)[/tex]