Answer:
We can use the formula for compound interest to calculate the amount and interest:
A = P * (1 + r/n)^(n*t)
I = A - P
Where:
P = Principal = $15,300
r = Rate = 8% = 0.08
n = Compounding frequency per year = 4 (since it is compounded quarterly)
t = Time period = 6 years
Plugging in the values, we get:
A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28
I = 23,659.28 - 15,300 = $8,359.28
Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.
I hope this helps.
what could be the value of the point grafted only number line between 0.09 and 0.10
1. A biologist hypothesizes that the mean life expectancy of a cockroach is 17 days. Researchers believe the true mean is less than 17 days and they plan a hypothesis test at the 10% significance level on a random sample of 80 of these cockroaches. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
A. μ = 9
B. μ = 10
C. μ = 17
D. μ = 20
E. μ = 21
2.Automobile tires can have a symmetric tread or an asymmetric tread. An experiment is to be conducted to determine whether the stopping distance is the same for both types of tire treads. In previous studies, it was determined that automobile size (small, medium, large) is associated with stopping distance, but automobile type (van, truck, SUV, and so on) is not associated with stopping distance. How could the experiment BEST be conducted?
A. By blocking on stopping distance
B. By blocking on tire tread type
C. By blocking on automobile type
D. By blocking on automobile size
E. Without blocking
3. A popular podcast wants to know the proportion of listeners that think assault weapons should be banned for civilians. Listeners are asked to text "Y" for yes or "N" for no to a provided number. Sixty-five percent of the 1,500 people that responded texted "Y." Which condition for inference has NOT been met?
A. All conditions appear to be met.
B. The sample is an SRS of the population.
C. N > 10n
D. np ≥ 10 and n(1 - p) ≥ 10
E. Inference about a proportion is the objective.
4.Fifteen pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown.
Which of the following conclusions is appropriate?
A. A line is an appropriate model to describe the relation between X and Y.
B. A line is not an appropriate model to describe the relation between X and Y.
C. The assumption of the Law of Averages has been violated.
D. The variables X and Y are not related at all.
E. There is not enough information about the variables X and Y to form a conclusion.
Lou is 1,200 feet from the base of a building that stands 500 feet tall. Assuming Lou's height is negligible, determine the angle of elevation from him to the top of the building. First, choose which angle represents the angle of elevation and then select the measure of that angle from the choices provided.
Select TWO correct answers.
We can see from the calculation that the angle of elevation of the building is 22.6 degrees.
Explain angle of elevation
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object that is above the observer's level. It is the upward angle from the observer's eye to the object being observed.
We have that;
Tan θ = 500/1200
θ = tan-1 (500/1200)
θ = 22.6 degrees
Thus the angle of elevation is obtained as 22.6 degrees as we can see here.
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People, I need to figure out a question
Is the sun of 7/10 + 1/5 closer to 0, 1/2 or 1?
Answer:
1
Step-by-step explanation:
7+10+1/5
7/10 = 0.7
1/5 = 0.2
0.7+0.2=0.9
Therefore it would be closest to 1.
Answer: 1
Step-by-step explanation:
To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer
if you are standing 350 feet away from a "1000" foot tall skyscraper, what angle of elevation is needed for you to look up and see the top of the building? when your angle of elevation is at 25 degrees you see your friend waving at the window. exactly how far apart are you?
Answer:
70.7°
350 feet
Im not too sure about the last one
The sum of two numbers is 998
The difference between them is 10
What are the two numbers?
Answer:
The two numbers are 494 and 504
Step-by-step explanation:
Let x = one of the numbers
Let y = the other number
x + y = 998
x - y = 10 or x = y + 10
Substitute y + 10 for x in the first equation and solve for y
x + y = 998
y + 10 + y = 998 Subtract 10 from both sides
y + y = 988 Combine like terms
2y = 988 Divide both sides by 2
y = 494
One of the numbers is 494.
x = y + 10 Substitute 494 for y
x = 494 + 10
x = 504
The other number is 504.
Check:
x + y = 998
504 + 494 = 998
998 = 998 checks
x - y = 10
504 - 494 = 10
10 = 10 checks
Helping in the name of Jesus.
Write the coordinates of the vertices after a reflection over the x-axis.
y
x
-10
10
-10
10
0
T
U
V
T(-1, 7)
→
T′(
,
)
U(-1, 8)
→
U′(
,
)
V(9, 6)
→
V′(
,
)
T(-1, 7)
→
T′(-1, -7)
U(-1, 8)
→
U′(-1, -8)
V(9, 6)
→
V′(9, -6)
What's the difference between $4 and 36 cents
Answer:
364 cents or $3.64
Step-by-step explanation:
We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.
400 - 36 = 364
Difference is 364 cents or $3.64
Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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Need help with number 1!! Pleaseee
Answer:
Step-by-step explanation: find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with 7 (use a calculator if needed)
College Trig Question!!!!!!!!!!!!!!
The equation, for the simple harmonic motion of a particle moving uniformly is s ( t ) = A x cos (ωt).
How to find the equation ?An object undergoing simple harmonic motion follows a periodic oscillation in a straight line, resembling a sinusoidal curve. Likewise, when an object continuously traverses upon a circle with uniform motion, its projection along the diameter travels back and forth in a simple harmonic motion pattern.
Assuming that the particle commences at the highest point of the simple harmonic motion at time t = 0, either the sine or cosine function is utilized to derive the equation for the simple harmonic motion formula. Thus, let us employ the cosine function in this instance:
s ( t ) = A x cos (ωt)
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Need this answer please and show work
The value of the "trigonometric-expressions' are :
(a) tan(5π/2) is undefined,
(b) sec(315°) is √2.
Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.
Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),
First, we convert 315° to radians:
Which is : 315° = (7π/4) radians;
Next, we find the value of cos(7π/4):
⇒ cos(7π/4) = cos(π/4) = (√2)/2;
Finally, we substitute in the identity for sec(θ);
So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.
Therefore, value of sec(315°) is √2.
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The given question is incomplete, the complete question is
Find the value of the trigonometric expressions :
(a) tan(5π/2)
(b) sec(315°)
What is the midpoint of the line segment with the given endpoints (4,6) (3,-3)
Help it’s urgent
The coordinates of the midpoints of the given line segment is:
(3.5, 1.5)
How to find the midpoints of a line segment?The midpoint of a line segment is simply referred to as the center of that specific line segment.
Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.
The coordinates of the endpoints of the line are:
(4,6) and (3,-3)
The formula to find the coordinates of the midpoint of the line is:
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Thus, we have:
(x, y) = (4 + 3)/2, (6 - 3)/2
= (3.5, 1.5)
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Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius = diameter/2 = 32/2 = 16 ft.
By substituting the parameters, we have:
Volume of cylinder, V = 3.14 × 16² × 10
Volume of cylinder, V = 8,038.4 cubic feet.
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Please Help With Question Inside of the picture
The workers percentile score is given as follows:
69.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The z-score for this problem is given as follows:
z = 0.5.
Hence the percentile score is of 69.15%, as z = 0.5 has a p-value of 0.6915.
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PLEASE HELP ITS DUE TOMORROW!!!
Answer:
Step-by-step explanation:
House
B) Down Payment: $151,800
C) $607,200
D) $819,720
E) $1,426,920
F) $47,564
Car:
B) $2,902.50
C) $16,447.50
D) $3,700.6875 = $3,700.69
E) $20,148.1875 = $20,148.19
F) $335.803125 = $335.80
DONE !!! :)
In circle S with
m
∠
R
S
T
=
102
m∠RST=102 and
R
S
=
6
RS=6 units, find the length of arc RT. Round to the nearest hundredth.
In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.
The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.
Rounded to the nearest hundredth, this is approximately 10.68 units.
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 29 ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sport coat.
The probability of Casey selecting a tie that goes well with the sport coat is 0.517.
The probability of Casey selecting a tie that does not go well with the sport coat is 0.483
What are the probability and the odds of the tie going well or not going well with the sport coat?The probability of Casey selecting a tie that goes well with the sport coat is:
P(goes well) = 15/29
P(goes well) ≈ 0.517
The probability of Casey selecting a tie that does not go well with the sport coat is:
P(does not go well) = 1 - P(goes well)
P(does not go well) = 1 - 15/29 = 14/29
P(does not go well) ≈ 0.483
The odds in favor of the tie going well with the sport coat are:
P(goes well) : P(does not go well) = 15/29 : 14/29
P(goes well) : P(does not go well) = 15:14
The odds against the tie going well with the sport coat are:
P(does not go well) : P(goes well) = 14/29 : 15/29
P(does not go well) : P(goes well) = 14:15
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The table shows the home state of the 175 high school students who attended a tri-state debate tournament. The ratio of Illinois students to Michigan students was 6:5. How many students were from Indiana?
Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:
Illinois students / Michigan students = 6/5
We can simplify this proportion by multiplying both sides by 5:
Illinois students = 6/5 * Michigan students
Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:
Illinois students + Michigan students + Indiana students = 175
We can substitute the expression we obtained for the number of Illinois students into this equation:
6/5 * Michigan students + Michigan students + Indiana students = 175
Multiplying both sides by 5 to eliminate the fraction, we get:
6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875
Combining like terms, we get:
11 * Michigan students + 5 * Indiana students = 875
Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:
Illinois students / Michigan students = 6/5
Substituting the values from the table, we get:
Illinois students / Michigan students = 24/20
Cross-multiplying, we get:
Illinois students * 20 = Michigan students * 24
Simplifying, we get:
Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students
Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.
Substituting this into the equation we obtained earlier, we get:
11 * 29 + 5 * Indiana students = 875
Solving for Indiana students, we get:
5 * Indiana students = 875 - 11 * 29 = 546
Dividing both sides by 5, we get:
Indiana students = 546/5 = 109.2
Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.
Therefore, the answer is 110 students from Indiana.
in the figure shown, the darker square is removed. Divide the remaining figure into two rectangles
The dimensions of each rectangle are x by (x- y) and y by (x - y); option A and D
The area of each rectangle is x² - 2xy + y² and x² - xy
The total area of the remaining figure is 2x² - 4xy + 2y²
This figure represents the difference of two squares in that x² - y² = (x + y)(x -y)
What is the are of each triangle?The area of each rectangle is:
x * (x- y) = x² -xy
and
y * (x - y) = xy - y²
The total area of the remaining figure is:
x² -xy + xy - y² = x² - y²
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You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2
HELP ME PLEASE AND SHOW WORK THANK YOU WILL MARK BRAINLIEST.
Based on the image, we can infer that the router cannot cover the kitchen area.
How to calculate if the router covers the living room and kitchen area?To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.
From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.
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If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=
The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and tangent to the curve at t=2.
In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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Christian earned a grade of 67% on his multiple choice science final that had a total of 200 problems. How many problems on the final exam did Christian answer correctly?
Answer: 134.
Step-by-step explanation:
First revert 67% into it's decimal form. You get 0.67. Then, multiply 0.67 by 200 because there were 200 problems.
0.67 x 200
67 x 2
134
So, christian got 134 out of 200 problems correct.
An oil candle globe made of hand-blown glass has a diameter of 25.8 cm. What is the volume of the globe? Use 3.14 for .
globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]
Lin has 9 plates she puts 1/4 of a sandwich on each plate which expression represents the sandwiches in the situation
A. 9x4
B. 9x1/4
C. 4x9
D. 4x1/9
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 14 gallons of fuel, the airplane weighs 2091 pounds. When carrying 48 gallons of fuel, it weighs 2312 pounds. How much does the airplane weigh if it is carrying 52 gallons of fuel?
The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds
Let,
Weight of airplane = y
Amount of fuel = x
The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.
It is given,
2091 = 14m + c ..... (1)
2312 = 48m + c ..... (2)
On subtracting, (1) with (2), we get
221 = 34m
m= (221/34)= 6.5
Now, on putting the value of (m) in (1), we get,
2091 = 14(6.5) + c
So,
c = 2000
Therefore, the linear equation can be written as,
y = (6.5)mx + 2000
Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.
That is,
y = (6.5)(52) + 2000
y = 2338
So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.
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HELP ME PLEASE!
Whoever answers right gets brainliest!
Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.
Here,
The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.
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Prepare the journal entry to record Jevonte Company's issuance of 29,000 shares of its common stock assuming the shares have a
a. $3 par value and sell for $16 cash per share.
b. $3 stated value and sell for $16 cash per share.
View transaction list
Journal entry worksheet
<
2
Record the issuance of 29,000 shares of common stock assuming the shares
have a $3 par value and sell for $16 cash per share.
Note: Enter debits before credits.
Transaction
General Journal
Cash
Common stock, $3 par value
Paid-in capital in excess
Debit
Credit
The journal entry to record the transaction is given:
Account Debit Credit
Cash $464,000
Common Stock, $3 par value $87,000
Paid-in capital in excess of par $377,000
What is a journal entry?A journal entry is used to record a business transaction in the accounting records of a business.
A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger
Assuming the shares have a $3 par value and sell for $16 cash per share:
Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000
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What is the answer for this problem and tell me how it is correct.
Answer:
Step-by-step explanation:
D is the correct answer.
Answer:
D
Step-by-step explanation:
By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.
A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.
B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.
C is not true because the art museum is located 1 unit east and 2 units north of the state capital.
This is why D is the correct answer.
8 is less than or equal to -3x +26
The solution is: x ≥ 6.
What is linear inequalities?
Linear inequality is an equation or expression that do not have a definite solution. Thus it consist of either of greater than, less than, greater than or equal to, less than or equal to etc.
In the given inequality question, we have;
8 is less than or equal to -3x +26
This can be expressed as;
8 ≤ -3x +26
so that collecting like terms,
8 - 26 ≤ -3x
-18 ≤ -3x
-18/ -3 ≤ x
6 ≤ x
Therefore, x ≥ 6.
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