The account will be worth approximately $13,268.58 in 20 years if it is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi-annually.
What is the accrued amount in 20 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $6,500
Compounded semi-annually n = 2
Time t = 20 years
Interest rate r = 3.6%
Accrued amount A = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 3.6/100
r = 0.036
Plug in the given values into the above formula.
A = P( 1 + r/n )^( n × t )
A = $6,500( 1 + 0.036/2 )^( 2 × 20 )
A = $6,500( 1 + 0.036/2 )^( 40 )
A = $6,500( 1 + 0.018 )^( 40 )
A = $13,268.58
Therefore, the accrued amount in 20 years is $13,268.58.
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In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1,007 adults to learn about their major healthcare concerns. The survey results showed that 575 of the respondents lack confidence they will be able to afford health insurance in the future.
(a)
What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to two decimal places.)
(b)
At 90% confidence, what is the margin of error? (Round your answer to four decimal places.)
(c)
Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to four decimal places.)
to
(d)
Develop a 95% confidence interval for this population proportion. (Round your answer to four decimal places.)
to
a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future is 0.57
b) At 90% confidence, the margin of error is 0.0324.
c) The 90% confidence interval is (0.5376, 0.6024).
d) The 95% confidence interval is (0.5314, 0.6086).
(a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future can be found by dividing the number of respondents who lack confidence (575) by the total number of respondents (1,007):
Point estimate = 575/1007 = 0.57 (rounded to two decimal places)
(b) The margin of error can be calculated using the formula:
Margin of error = z√(p'(1-p')/n)
where z is the z-score associated with the desired level of confidence, p' is the point estimate, and n is the sample size. For a 90% confidence level, the z-score is 1.645.
Margin of error = 1.645√(0.57*(1-0.57)/1007) ≈ 0.0324 (rounded to four decimal places)
(c) The 90% confidence interval can be calculated using the formula:
Point estimate ± Margin of error
Substituting the values:
0.57 ± 0.0324
The 90% confidence interval is (0.5376, 0.6024) (rounded to four decimal places).
(d) The 95% confidence interval can be calculated in the same way, but with a different z-score. For a 95% confidence level, the z-score is 1.96.
Margin of error = 1.96√(0.57(1-0.57)/1007) ≈ 0.0386 (rounded to four decimal places)
0.57 ± 0.0386
The 95% confidence interval is (0.5314, 0.6086) (rounded to four decimal places).
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please show work asap thankyou so much
The net sales, =$20.98
The Goods available for sales= $2,045
The total cost of Goods sold=$1,955
Gross profit =$1,934.02
Net income = $1,395.98
How to determine the net sales from the last month's business income statement?The operating income (sales) = $7,240
The return on sales (ROS) = $345
The net sales (revenue generated) = ?
But ROS = operating income/net sales
Net sales = 7240/345;
= $20.98
The goods available for sale = beginning inventory+ new purchase = $725+$1320 = $2,045.
The total cost of Goods sold = Beginning inventory+goods available for sale - end inventory.
= 725+2,045- 815
= 2770-815
= $1,955
The gross profit = cost of goods sold (COGS) - total revenues.
= $1,955-$20.98
= $1,934.02
Net income = total operating expenses - gross profit
operating expenses = 1,750+1000+280+150+150 = $3,330
gross profit = $1,934.02
Net income = 3,330-1,934.02 = $1,395.98
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I need help on these
The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
What are the radius and diameter properties of a circleA circle is a two-dimensional shape that is defined as a set of points that are equidistant from a single fixed point, called the center. The radius of a circle is the distance from the center to any point on the circumference. All radii of a circle are equal in length. While the diameter of a circle is a straight line passing through the center of the circle and touching two points on the circumference. The diameter is always twice the length of the radius.
For question (9):
the segments indicated as x and 6 are radii of the circle so;
x = 6
For question (10):
the radius = 31.6/2 = 15.8
also;
the radius = 6.9 + x
so;
x = 15.8 - 6.9
x = 8.9.
Therefore, the The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
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9. What is the measure of ZHLI?
H
K
30°
The missing angle of the given image is: ∠HLI = 150°
How to find the measure of the missing angle?There are different terms in this type of case when looking for missing angles and they include:
Corresponding angles
Supplementary angles
Opposite angles
Alternate angles
Now, we are given that:
∠JLI = 30°
We know that the sum of angles on a straight line is 180°. Thus:
∠HLI = 180° - 30°
∠HLI = 150°
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The approximate areas of Nebraska and Massachusetts are listed below:
Nebraska: 2 x 105 square kilometers
Massachusetts: 2.73 x 104 square kilometers
What's the difference between the areas of the two states? Express your answer using
either standard notation or scientific notation.
The distance between the areas of the two states is A = 1.727 x 10⁵ km²
Given data ,
Let the area of Nebraska = 2 x 10⁵ km²
Let the area of Massachusetts = 2.73 x 10⁴ km²
The difference between the areas of Nebraska and Massachusetts A = the area of Nebraska - the area of Massachusetts
On simplifying the exponents , we get
A = 2 x 10⁵ km² - 2.73 x 10⁴ km²
Taking the common factor , we get
A = 10⁴ ( 20 - 2.73 )
A = 10⁴ ( 17.27 )
A = 1.727 x 10⁵ km²
Hence , the area is A = 1.727 x 10⁵ km²
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Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x? Left-brace StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction Right-brace Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace Left-brace StartFraction pi over 6 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
Given that:
sin(2x) – sin(x) = 0
Simplify the equation, then the value of 'x' is calculated as,
sin(2x) – sin(x) = 0
sin(2x) = sin(x)
2 sin x cos x = sin x
cos x = 1/2
cos x = cos (π/3, 5π/3)
x = π/3, 5π/3
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
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In the following diagram, ABCDABCD is a square. The coordinates of the vertices A,B,CA,B,C and DD are (3,3),(8,3),(8,8)(3,3),(8,3),(8,8) and (3,8)(3,8) respectively.
The square is dilated from the origin by a factor of 1111 to give A′B′C′D′A′B′C′D′.
What are the coordinates of point C′C′? (NEED THIS ASAP)
Answer:
Step-by-step explanation:
To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.
The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:
x-coordinate of C' = 1111 * 8 = 8888
y-coordinate of C' = 1111 * 8 = 8888
Therefore, the coordinates of point C' are (8888, 8888).
What transformation maps the pre-image (red) onto the image (blue)?
O reflection
O glide reflection
O rotation
O translation
Answer: Translation
Step-by-step explanation:
To get from the pre-transformation shape (red) to the transformed image (blue), a translation takes place. This is where the shape is not rotated, reflected, or stretched, but simplify "slided" or "shifted" somewhere else.
Helppp me please what is the formula for the carton 1/2*base of triangle*height of prism*height of prism ?
The volume of the triangular prism in the diagram is 10.5 in³
Calculating the volume of a triangular prismFrom the question, we are to calculate the volume of the the given prism.
The given prism is a triangular prism.
Volume of a triangular prism = Area of triangle × Height of prism
Thus,
Volume of the triangular prism = 1/2 × Base of triangle × Height of triangle × Height of prism
From the given diagram,
Base of triangle = 2 in
Height of triangle = 1.5 in
Height of prism = 7 in
Volume of the triangular prism = 1/2 × 2 in × 1.5 in × 7 in
Volume of the triangular prism = 10.5 in³
Hence,
Volume of the triangular prism is 10.5 in³
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Complete the ratio table.
Answer:
55
70
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
55 and 70
Step-by-step explanation:
5÷2=2.5
20÷8=2.5
45÷18=2.5
so
22×2.5=55
and
28×2.5=70
What is the solution to the given linear-quadratic system: y = x + 5 and y = x² + 5?
Answer: 1 over 6
Step-by-step explanation:
Look at the figure shown. Which angle is obtuse?
Angle CDA.
Angle BAD.
Angle CBA.
Angle DAB.
A
60
B
120
120
C
60
D
The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°
What is an obtuse angle?An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are
90° < x < 180°
From the given question, we are to determine the angle which obtuse.
In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.
The angle that is greater than 90° but less than 180° is 120°.
Thus,
The obtuse angle is the angle that measures 120°
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PLEASE I REALLY NEED THIS HELP
solve the triangle. round to the nearest tenth
The correct solution of the triangle is seen in option D
How do you solve the triangle?In this case, we would need to use the sine rule so as to solve the triangle as we have in the problem that is before us here. The sine rule states that;
a/Sin A = b/SinB = c/SinC
We know that we can be able to obtain the angle C using the sine rule;
29/Sin 42 = 33/SinC
SinC = 33Sin42/29
C = Sin-1(33Sin42/29)
C = 49.6 degrees
The angle B is now;
180 - (42 + 50)
B = 88.4 degrees
Then;
b/Sin 88 = 29/Sin42
b = 29 Sin 88/Sin42
b = 28.98/0.669
b = 43.3
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Find the surface area of the figure below. Round to the nearest 10th.
The surface area of the given composite figure is: 484.38 cm²
How to find the surface Area?The formula for the area of a rectangle is:
Area = Length * Width
The formula for the area of a square is:
Area = side * side
The surface area is simply the area of each of the surfaces of the figure.
Thus, surface area of the given composite figure is:
4(13 * 10) + (10 * 10) + (10 * 10) - 3π(5²))
= 484.38 cm²
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Ice Mountain Ski Resort is Philip's favorite place to go in the winter. This year, his aunt bought him a season pass. Philip used his season pass discount to get $13.75 off of the price of a new helmet. After the discount, the helmet's price was $116.25.
Answer:
$130
Step-by-step explanation:
price of helmet =discount+ price after discount
=$13.75+$116.25
=$130
Helpp please guyssssss
Answer:
The answer and step by step explanation is above
2. Marshall wants to save at least $175
for a new video game system and
some games. So far, he has saved
$68.50.
Part A
Write an inequality to represent the
amount of money, a, that Marshall still
needs to save.
Part B
Solve the inequality. Which of the
following describes how much money
Marshall still needs to save?
A He needs to save at least $106.50
more.
B He needs to save at most $106.50
more.
He needs to save at least $243.50
more.
D He needs to save at most $243.50
more.
The solutions to the inequality word problem are:
2) a + $68.50 ≥ $175
3) A He needs to save at least $106.50 more.
How to solve Inequality word problems?2) We are told that Marshall wants to save at least $175 for a new video game system and some games.
So far, he has saved $68.50.
If the amount of money he needs to save extra is a, then the inequality we have:
a + $68.50 ≥ $175
3) a + $68.50 ≥ $175
subtracting $68.50 from both sides gives:
a ≥ 175 - 68.5
a ≥ $106.5
He needs to save at least $106.50 more.
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What is the base of the following natural logarithm?
In(x)
O 1
O 10
O e
The base of the natural logarithm ln(x) expression is 10
What is the base of the natural logarithm?From the question, we have the following parameters that can be used in our computation:
ln(x)
The base of the above expression is not stated
The general rule of logarithm is that when the base of the expression is not stated, then the base is 10
If the base of the expression is stated, then the expression would take the form
lnₐ(x), where the base is represented with the variable a
This means that the base of the natural logarithm ln(x) expression is 10
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If 5, x, y, and 40 are in geometric progression find x and y respectively
The values of x and y in the geometric progression are 10 and 20
Finding x and y in the geometric progressionFrom the question, we have the following parameters that can be used in our computation:
5, x, y, and 40
To calculate the values of x and y, we have
x/5 = 40/y
Cross multiply
So, we have
xy = 200
Set x = 10
So, we have
10y = 200
This gives
y = 20
So, we have
10/5 = 40/20 = 2 --- true
Hence, x is 10 and y is 20
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The US Fish and Wildlife Service reported that the mean length of a 6 year old trout in the Arolik River in Alaska is 480 and standard deviation of 40 mm. Assume length of trout is normally distributed,
a) Find the 58th percentile of the lengths
The 58th percentile of the lengths is 489.4 mm.
What is the 58th percentile of the lengths?The 58th percentile of the lengths is calculated from normal distribution curve as shown below.
The mean of the distribution is at the 50th percentile.
The 58th percentile is between the mean and 1 standard deviation above the mean.
Mean (50%) = 480 mm
58% = ?
1 standard deviation above the mean (84%)= M + S.D = 480 mm + 40 mm = 520 mm
We are going to interpolate, to find the approximate value of the length.
50 ----- 480 mm
58 ----- ?
84 ------- 520 mm
(58 - 50)/(84 - 50) = (x - 480)/(520 - 480)
0.235(40) = x - 480
9.4 = x - 480
x = 489.4 mm
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What fraction is equal to 15/18
Please help me with these 6th grade math questions.
Answer:
1. s < 40
2. w ≤ 12
3. D ≥ 110
4. D ≤ 3 1/2
5. w ≥ 30
6. m ≥ 45
7. t ≠ 21
8. c < 45
9. D > 1/5
10. s ≠ 45 5/6
11. h ≥ 48
12. P ≠ 5
The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin's weight differs most from the value predicted by this model?
The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
Let's elaborate the model this way:
Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft
Snowflake's weight - Pax's weight = 549 - 519 = 30 lb
Ratio = 30/0.6 = 50 lb/ft
This means that for every foot of length, the dolphin has a variable weight of 50 lb.
However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:
Snowflake = 50 × 8.2 = 410
Pax = 50× 7.6 = 380
Snowflake = Actual weight - Ratio× Length = 549 - 410 = 139
Pax = Actual weight - Ratio × Length = 519 - 380 = 139
The common difference is 139.
Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:
y = 139 + 50x
Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:
Blaze y = 139 + 50 × 6.8 = 479 ⇒ difference of 9 lb (488 - 479)
JoJo y = 139 + 50 × 5.8 = 429 ⇒ difference of 31 lb (460 - 429)
Corky y = 139 + 50 ×8.4 = 559 ⇒ difference of 2 lb (559 - 557)
Shadow y = 139 + 50 × 7.4 = 509 ⇒ difference of 8 lb (509 - 501)
Hence, the dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
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The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to
create a linear model that predicts the weight (y) of a dolphin given its length (X). Which dolphin's weight differs most from th
value predicted by this model?
Name
Snowflake
Shadow
Corky
Pax
JoJo
Blaze
Length (ft)
8.2
74
8.4
7.6
5.8
6.8
Weight (lb)
549
501
557
519
460
488
Blaze
JOJO
Corky
Shadow
What is the style of William Holman Hunt's The Awakening Conscience (1853)?
Pre Raphaelite
Impressionism
Nabis
Realism
Answer:
The style of William Holman Hunt's The Awakening Conscience (1853) is Pre-Raphaelite.
Write the equation for an exponential function, in the form ya x b. whose graph passes through the coordinate points (2, 12) and (3, 24).
The calculated equation for the exponential function is y = 3(2)ˣ
Calculating the equation for the exponential functionFrom the question, we have the following parameters that can be used in our computation:
Points = (2, 12) and (3, 24)
By definition, as exponential function is represented as
y = abˣ
Substitute the known values in the above equation, so, we have the following representation
ab² = 12
ab³ = 24
So, we have
b = 2
This means that
a(2)³ = 24
So, we have
a = 3
Recall that
y = abˣ
So, we have
y = 3(2)ˣ
Hence, the equation for the exponential function is y = 3(2)ˣ
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The data shown are the number of grams per serving of 30 selected brands of
cakes. Construct a frequency distribution using 5 classes.
32 47 51 41 46 30
46 38 34 34 52 48
48 38 43 41 21 24
25 29 33 45 51 32
32 27 23 23 34 35
The given data results in the following Frequency Distribution
Class Frequency
21-27 3
28-34 8
35-41 7
42-48 8
49-55 4
In statistics, frequency distribution is a way of organizing data into categories, or intervals, and counting how many observations fall into each category. It helps us understand the distribution of data and identify patterns within it.
To construct a frequency distribution using 5 classes, we need to first determine the range of the data:
Range = Maximum value - Minimum value
= 52 - 21
= 31
We can then calculate the width of each class:
Width = Range / Number of classes
= 31 / 5
= 6.2
Since we cannot have a fractional width, we round up to the nearest whole number. The class width is therefore 7.
Next, we need to determine the class intervals, or boundaries, which are the values that define each class. We start with the minimum value and add the class width successively:
Class 1: 21-27
Class 2: 28-34
Class 3: 35-41
Class 4: 42-48
Class 5: 49-55
We can now count how many observations fall into each class. The resulting frequency distribution is shown below:
Class Frequency
21-27 3
28-34 8
35-41 7
42-48 8
49-55 4
In this frequency distribution, we can see that the majority of the observations fall into the middle three classes, with fewer observations in the first and last classes. This suggests that the data is roughly symmetric and evenly distributed around the center.
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I WILL GIVE 35 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE
Answer:
F1 8,-2 F2 -5,-3
Step-by-step explanation:
if A C B, then A n B = A U B
1) sometimes
2) never
3) always
if A C B, then A n B = A U B is always true
How to determine if A C B, then A n B = A U BThe statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".
Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.
On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.
Therefore, we have:
A n B = A (since all the elements of A are in both A and B)
A U B = B (since A is a subset of B)
So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true
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A hot air balloon is currently 100 feet above ground. After 5 minutes, the hot air balloon is 40 feet above ground. Write an equation
Answer:
100 + 5f = 40
5f = -60
f = -12 feet per minute (decrease of 12 feet per minute)
Which linear equation is represented in the graph?
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
The equation of the line passing through the given points is y = -2x+1.
Given that is a line passing through two points (0, 1) and (2, -3) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 1) and (2, -3),
Therefore, the required equation is =
y-1 = -3-1/2 (x-0)
y-1 = -2x
y = -2x+1
Hence, the equation of the line passing through the given points is y = -2x+1.
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