Answer:
80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
Step-by-step explanation:
We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;
Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.
Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex] = 4.61
n = sample of people = 20
[tex]\mu[/tex] = true average number of hours of TV watched per week
Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.
So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;
P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80 {As the critical value of t at 19 degrees of
freedom are -1.33 & 1.33 with P = 10%}
P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80
P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]
= [8.28 hours, 11.02 hours]
Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
A student is interested in becoming an actuary. The student knows that becoming an actuary takes a lot of schooling and will have to take out student loans and wants to make sure the starting salary will be higher than $55,000/year. The student takes a random sample of 30 starting salaries for actuaries and finds a p-value of 0.0392. Use α = 0.05.
a. Choose the correct hypotheses.
H0:μ≠55,000 H1:μ=55,000
H0:μ>55,000 H1:μ≤55,000
H0:μ<55,000 H1:μ≥55,000
H0:μ=55,000 H1:μ>55,000
H0:μ=55,000 H1:μ≠55,000
H0:μ=55,000 H1:μ<55,000
b. Should the student pursue an actuary career?
No, since we can reject the null hypothesis
No, since we can reject the claim
Yes, since we can reject the claim
Yes, since we can can reject the null hypothesis
Answer:
a) H0:μ=55,000 H1:μ>55,000
b) Yes, since we can can reject the null hypothesis
Step-by-step explanation:
a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For this case;
Null hypothesis is that the starting salary will be equal to $55,000/year.
H0:μ=55,000
Alternative hypothesis is that the starting salary will be greater than $55,000/year.
H1:μ>55,000
b) Decision Rule;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
For this case;
P-value = 0.0392
α = 0.05
Since P-value < 0.05, we can reject null hypothesis.
Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.
- Yes, since we can can reject the null hypothesis
The longer leg of a 30-60-90° triangle is 18. What is the length of the other leg?
A) 1213
B) 93
C) 9
D) 63
Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:
[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]
Hope this helps!
The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. A graph on a coordinate plane titled Distance Remaining Over Time. The x-axis is labeled time (in hours), numbered 1 to 8, and the y-axis is labeled miles to destination, numbered 50 to 400. A straight line with a negative slope starts at point (0, 350) and ends at point (7, 0). Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Answer:
For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
The point (0, 350) tells you Michelle's trip is 350 miles long. The point (7, 0) tells you she completed it in 7 hours. The point (6, 50) on the graph tells you she has 50 miles remaining of the original 350 after 6 hours.
True: for each hour Michelle drove, she traveled an additional 50 miles.
Answer:
B. For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
If we rotate the 3-D figure around y-axis we'll obtain a cone with a radius of 3 units
If sin(θ -π/2) = 0.73.. find cos (-θ) plz explain how to solve
Answer:
[tex]cos(-\theta) = -0.73[/tex]
Step-by-step explanation:
It is given that:
[tex]sin(\theta -\dfrac{\pi}{2}) = 0.73[/tex]
Formula to be used:
[tex]1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx[/tex]
Using Formula (1) written above:
[tex]\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)[/tex]
Now, using Formula (2) written above:
[tex]\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta[/tex]
So, we can say that:
[tex]sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)[/tex]
We have to find the value of [tex]cos(-\theta)[/tex].
Using Formula (3) written above:
[tex]cos(-\theta) = cos\theta[/tex]
So, ultimately we need to find the value of [tex]cos\theta[/tex]
Using equation (1):
[tex]-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73[/tex]
So, the answer is [tex]cos(-\theta) = -0.73[/tex].
What is the value of X ?
Answer:
D
Step-by-step explanation:
2² + 6² = x²
4 + 36 = x²
40 = x²
x = 2√10
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
A student used multiple regression analysis to study how family spending (y) is influenced by income
(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousands
of dollars. The following results were obtained.
ANOVA
df SS
Regression 3 45.9634
Residual 11 2.6218
Total
Coefficients Standard Error
Intercept 0.0136
x1
0.7992 0.074
x2
0.2280 0.190
x3
-0.5796 0.920
a. Write out the estimated regression equation for the relationship between the variables. (1
mark)
b. Compute coefficient of determination. What can you say about the strength of this
relationship? (3 marks)
c. Carry out a test to determine whether y is significantly related to the independent variables.
Use a 5% level of significance. (3 marks)
d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
Answer:
Step-by-step explanation:
Hello!
Given the variables
Y: family spending
X₁: income of a family
X₂: family size
X₃: additions to savings of a family
And the regression output (see attachment)
The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃
a)
To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)
The estimated regression equation is:
^Y= a + b₁X₁ + b₂X₂ + b₃X₃
^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
b)
Using the SS information you can calculate the coefficient of determination as:
SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852
[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]
R²= 94.6%
This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
c)
The hypotheses are:
H₀: β₁= β₂= β₃= 0
H₁: At least one βi≠0 ∀ i=1, 2, 3
α: 0.05
The statistic for the multiple regression is
[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]
[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]
[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]
[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]
p-value < .00001
At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.
d.
Individual tests:
There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]
Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:
If p-value ≤ α ⇒ Reject null hypothesis.
If p-value > α ⇒ Do not reject the null hypothesis.
1)
H₀: β₁ = 0
H₁: β₁ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]
p-value < .00001 ⇒ Decision is to reject the null hypothesis.
2)
H₀: β₂ = 0
H₁: β₂ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]
p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.
3)
H₀: β₃ = 0
H₁: β₃ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]
p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.
So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.
I hope this helps!
A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)
Answer:
28.26 (Please mark as brainiest if you find it helpful )
Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.
Area of circle = pi * r ^ 2
⇒ 3.14 * (3) ^ 2 → 3.14 * 9
⇒ 28.26
A sphere and a cylinder have the same radius and height.the volume of the cylinderis 48cm3
Answer:
32 cm^3.
Step-by-step explanation:
Formulas for calculating:
sphere's volume - ;[tex]V_{sphere}=\frac{4\pi r^3}{3}[/tex]
cylinder's volume - .[tex]V_{cylinder}=\pi r^2 h[/tex]
Note that h=2r (height of the sphere consists of two radius).
Then [tex]V_{cylinder}= \pi r^2 h=\pi r^2 2r= 2\pi r^3[/tex]
Since [tex]V_{sphere}= \frac{4\pi r^3}{3}[/tex]
on calculating we get
[tex]V_{cylinder}= \frac{3V_{sphere}}{2}\\ \Rightarrow V_{sphere}=\frac{2V_{cylinder}}{3} =\frac{2\times48}{3} =32 cm^3[/tex]
If z=32 and z/2+37=x what is x
Answer:
53
Step-by-step explanation:
Plugging in 32 for z, you get:
(32)/2+37=x
16+37=x
x=53
Hope this helps!
The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
z/2 + 37 = x
Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be
x = 32/2 + 37
x = 16 + 37
x = 53
Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
A box is a cuboid with dimensions 28cm by 15cm by 20cm all measured to the nearest centimetre.
Disc cases are cuboid which measure 1.5 by 14.2 cm by 19.3 cm all measure to the nearest millimetre. Show that 17 disc cases, stacked as shown, will definitely fit the box
Answer:
The 17 disc cases would definitely fit into the box.
Step-by-step explanation:
The given cuboid box has the dimensions 28cm by 15cm by 20cm.
Disc cases are cuboid with dimensions 1.5cm by 14.2cm by 19.3cm.
volume of a cuboid = length × width × height
Volume of the box = 28 × 15 × 20
= 8400 cubic centimeters
Volume of each disc case = 1.5 × 14.2 × 19.3
= 411.09 cubic centimeters
When the 17 disc cases are stacked it would have a volume.
The volume of 17 disc cases = 17 × volume of a case
= 17 × 411.09
= 6988.53 cubic centimeters
Thus comparing the volume for 17 disc cases and that of the cuboid box, the disc cases would definitely fit into the box.
i.e = [tex]\frac{volume of box}{volume of 17 disc cases}[/tex]
= [tex]\frac{8400}{6988.53}[/tex]
= 1.20
Answer:
Step-by-step explanation:
27.5×14.5×19.5 =7775.625 cm³
1.55 x 14.25 x 19.35=427.393125
427.393125 x 17=7265.683
7775.625>7265.683
19.5x27.5x14.5=7775.625
1.45x14.15x19.25=394.961875
394.961875x17=6714.35
7775.63>6714.35
1.55x17=26.35
27.5>26.35
What is the range of g(x)=-1/2|x-6|+1
Answer:
The answer is A: ( - ∞, 1 )
Step-by-step explanation:
linear function for f(-11)=5, slope of f= -2/3
Answer:
f(x) = -2/3(x +11) +5
Step-by-step explanation:
The point-slope form of the equation of a line will give you the desired linear function:
y = m(x -h) +k . . . . . for slope m through point (h, k)
You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...
f(x) = -2/3(x +11) +5
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean salary of city 1 librarians
x2 = sample mean salary of city 2 librarians
s1 = sample standard deviation for city 1
s2 = sample standard deviation for city 2
n1 = number of soles for city 1
n1 = number of soles for city 2
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28
z = 2.048
x1 - x2 = 28,900 - 30,300 = - 1400
Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)
= 1647
The upper boundary for the confidence interval is
- 1400 + 1647 = 247
The lower boundary for the confidence interval is
- 1400 - 1647 = - 3047
A hiker starts at an elevation of 65 feet and descends 30 feet to the base camp . What is the elevation of the base camps ?
Answer:
the elevation of base camp is 35 ft
Step-by-step explanation:
Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation
Answer:
35 feet
Step-by-step explanation:
65 feet- 30 feet= 35 feet is the elevation of the base
What’s the correct answer for this?
Answer:
1) Antonio's statement
2) <A = 123
Step-by-step explanation:
1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.
2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)
Now
7x+5 = 180
7x = 175
x = 25
<A = 5x-2
= 5(25)-2
= 125-2
= 123
Please answer this correctly
Answer:
17.85 feet.
Step-by-step explanation:
Area = 1/4 * 3.14 * r^2 where r is the radius
So r^2 = 19.625 / (1/4 * 3.14)
r^2 = 25
r = 5 feet.
The perimeter = 2r + 1/4 * 2* 3.14*r
= 2*5 + 7.85
= 17.85 feet.
use the graph of y = tan x to find the value of y = tan 0. round to the nearest tenth of necessary. if the tangent is undefined at that point, write undefined.
a. 0.4
b. 0
c. -0.4
d. 1
Step-by-step explanation:
The graph of y = tan x is shown. We need to find what y equals when x = 0 (because in y = tan 0, x is replaced with 0)
So you can either find where x = 0 on the graph, or you can take the tangent of 0 to find your answer.
The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0 and this can be determined by using the given graph.
Given :
The graph of [tex]y = \tan x[/tex].
The following steps can be used to determine the value of [tex]y = \tan 0[/tex] :
Step 1 - The graph of the trigonometric function [tex]y = \tan x[/tex] is given.
Step 2 - According to the given graph, at (x = 0) the value of y is also 0.
Step 3 - So, the value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is:
[tex]y = \tan 0[/tex]
[tex]y = 0[/tex]
The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0.
For more information, refer to the link given below:
https://brainly.com/question/14375099
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Step-by-step explanation:
For this case we know that the distribution of the temperatures have the following parameters:
[tex] \mu = 98.19, \sigma =0.61[/tex]
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
Part b
We can calculate the number of deviations from the mean with the z score with this formula:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And using this formula we got:
[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
what is the last three
Answer:
20:30 goes to 8:12
the rest goes to 6:18
Step-by-step explanation:
i may be wrong
Answer:
7:12 is equivalent to 6:18
20:30 is equivalent to 8:12
5:15 is equivalent to 6:18
Step-by-step explanation:
plz mark brainliest
Item 5 Item 5
You are earning an average of $47,400 and will retire in 10 years. If you put 20% of your gross average income in an ordinary annuity compounded at 7% annually, what will be the value of the annuity when you retire?
Answer: the value of the annuity when you retire is $130919
Step-by-step explanation:
We would apply the future value which is expressed as
FV = C × [{(1 + r)^n - 1}/r]
Where
C represents the yearly payments.
FV represents the amount of money
in your account at the end of 10 years.
r represents the annual rate.
n represents number of years or period.
From the information given,
r = 7% = 7/100 = 0.07
C = 20/100 × 47400 = $9480
n = 10 years
Therefore,
FV = 9480 × [{(1 + 0.07)^10 - 1}/0.07]
FV = 9480 × [{1.967 - 1}/0.07]
FV = 9480 × 13.81
FV = $130919
A tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?
Answer:
after three years
Step-by-step explanation:
Please answer this question I give brainliest thank you! Number 9
Answer:
B
The mode is 11 and 3
The Median is 10
The mean is 12
Consider two unique parallel lines. What aspects of
these two lines are the same? What aspects of these two
lines would have to be different? Explain your reasoning.
Answer:
The slope of two parallel lines will always be the same. If the slope was slightly different, then the lines would intersect at some point, which breaks the definition of parallel lines.
The y-intercepts of two parallel lines have to be different, or else the two lines would be the same line. If the y-intercept and the slope are the same, then the lines will essentially equal each other.
Answer:
Sample Response: Two parallel lines will have the same slope. The slopes of parallel lines have to be equal. The y-intercepts of those two lines have to be different, otherwise they would be the same line. The x-intercepts of the parallel lines would also be different.
Step-by-step explanation:
edge 2020
the terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian
Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
What is the terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.
The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,
[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]
Multiply it with π/180 to find the measure of the angle in radian.
[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]
Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
Learn more about the terminal side of an angle here
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A family of five rents a kayak and splits the total time, k, equally. Each family member spent less than 25 minutes kayaking. Which values can be used to complete the math sentence below so that it accurately represents the situation?
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Edg.
Answer:
k ÷ 5 < 25
Step-by-step explanation:
A rectangular fish tank is 50 cm long, 40 cm wide, and 20 cm high. a) How many cubic centimeters of water will the tank hold? b) How many milliliters of water will the tank hold? c) How many liters of water will the tank hold?
Answer:
40 litres
Step-by-step explanation:
V = l x w x h
50 x 40 x 20 = 40000
40000 cm^3
1cm^3 = 1ml
40000 cm^3/ 1cm^3 = 40000ml
40000 x 10^-3 = 40 litres
Which is the best estimate of 90/7 divided by 1 3/4
Answer:
90/4= 12.9
1*3/4= 0.75
Step-by-step explanation:
