Answers
Answer:
Step-by-step explanation:
In the given figure, the triangle ABC is a right triangle with a right angle at C. We need to find the length of the side AB.
Using the Pythagorean theorem, we know that in a right triangle with sides of length a, b, and c (where c is the hypotenuse), we have c^2 = a^2 + b^2.
In this case, we have AC = 4 and BC = 3. So, applying the Pythagorean theorem, we get:
AB^2 = AC^2 + BC^2
AB^2 = 4^2 + 3^2
AB^2 = 16 + 9
AB^2 = 25
Therefore, AB = 5.
Related Questions
Use spherical coordinates to evaluate the triple integral ∫∫∫Ex2+y2+z2dV
, where E is the ball: x2+y2+z2≤81
.
Answers
[ rate 5stars~ and give thanks for more po! welcome! ]
Step-by-step explanation:
We have the triple integral:
∫∫∫E x^2 + y^2 + z^2 dV
where E is the ball x^2 + y^2 + z^2 ≤ 81.
In spherical coordinates, the volume element is given by:
dV = ρ^2 sin φ dρ dθ dφ
where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).
Substituting into the integral, we get:
∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ
= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π
= (2π/5)(9^5)(-(-1 - 1))
= (4π/5)(9^5)
≈ 114413.73
Therefore, the value of the triple integral is approximately 114413.73.
point(s) possible
Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1093 and x = 538 who
said "yes." Use a 90% confidence level.
Click the icon to view a table of z scores.
b) Identify the value of the margin of error E.
(Round to three decimal places as needed.)
c) Construct the confidence interval.
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
OA. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the
true value of the population proportion.
OB. 90% of sample proportions will fall between the lower bound and the upper bound.
C. One has 90% confidence that the sample proportion is equal to the population proportion.
D. There is a 90% chance that the true value of the population proportion will fall between the lower bound and the
upper bound.
Answers
standard error = sqrt((p-hat * (1 - p-hat)) / n)
where p-hat is the sample proportion.
Substituting the given values:
p-hat = x / n = 538 / 1093 = 0.4925
standard error = sqrt((0.4925 * (1 - 0.4925)) / 1093)
standard error ≈ 0.015
b) To find the margin of error, we can use the formula:
margin of error = z* * standard error
where z* is the z-score corresponding to the desired confidence level.
Since we are using a 90% confidence level, the z-score is 1.645 (see the table of z-scores).
Substituting the values:
margin of error = 1.645 * 0.015
margin of error ≈ 0.025
Therefore, the margin of error is approximately 0.025.
c) The confidence interval can be constructed using the formula:
confidence interval = p-hat ± margin of error
Substituting the given values:
confidence interval = 0.4925 ± 0.025
confidence interval = (0.4675, 0.5175)
Therefore, the 90% confidence interval for the proportion of people who feel vulnerable to identity theft is (0.4675, 0.5175).
d) The correct statement that interprets the confidence interval is:
OA. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
This statement means that if we repeated the sampling process many times and constructed a 90% confidence interval each time, approximately 90% of the intervals would contain the true proportion of people who feel vulnerable to identity theft.
Will give brainliest if you get correctly!
Guessing = Report
Answers
Answer:
Step-by-step explanation:
ASAP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answers
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
What is the greatest commen factor of 72 and 96
Answers
the greatest common factor of 72 and 96 is 24
$550 is deposited in an account with 8.5%
interest rate, compounded continuously.
What is the balance after 6 years?
F = $[?]
Answers
the balance after 6 years is approximately $926.45.
What is Continuous compounding ?
Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.
We can use the formula for continuous compounding to find the balance after 6 years:
[tex]F = Pe^{(rt)}[/tex]
where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.
[tex]F = 550e^{(0.085*6)}[/tex]
F ≈ $926.45
Therefore, the balance after 6 years is approximately $926.45.
To know more about Continuous compounding visit,
https://brainly.com/question/30460031
#SPJ1
Find the sales tax. Then find the total cost of the item.
$50.00
Sales Tax
Rate of Sales Tax Sales Tax
7%
?
Answers
As a result, the item's final price is $53.50 and the sales tax is $3.50.
What is sales tax?The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax
We can multiply the item's price by the applicable sales tax rate to determine the sales tax:
Price of Item x Sales Tax Rate equals Sales Tax
Sales Tax: $50.00 x 7% = $3.50
We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:
Price of Item + Sales Tax = Total Cost
$50.00 plus $3.50 equals $53.50 as a total
To know more about sales tax visit :
brainly.com/question/29751934
#SPJ1
Tell whether the given side lengths can represent the sides of a right triangle
10, 12, 20
Determine if the segment lengths form an acute, right, or obtuse triangle,
10, 11, 14
26.
Need help with all of these please need this asap. Please show work
Answers
23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]
24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex] and finally the side length opposite the [tex]60^\circ[/tex] is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.
So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]
25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20
For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.
Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.
26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.
what is the product of -6
Answers
Answer:
The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.
Step-by-step explanation:
if you rotate cars tires at 10,000 miles, if a car tire has 25,200 rotations per day, how many weeks will it be until you rotate the tires
Answers
It will take 4. 09 weeks for the tires to be rotated at the current rate.
How to find the time till rotation ?When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.
25, 200 rotations / day x 7 days / week = 176, 400 rotations per week
To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:
C = 2πr
Rotation per mile is:
1 mile / 87.96 inches / rotation = 72.26 rotations / mile
Number of weeks:
10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations
722, 600 rotations / 176, 400 rotations/week = 4.09 weeks
Find out more on tire rotations at https://brainly.com/question/3471381
#SPJ1
Jen works for a cellular phone company. She earns a salary of $250 per
week plus a bonus of 10% of the value of any phones and accessories
that she sells. In the past four weeks, Jen sold $312 worth of phones
and accessories.
Circle the amount that correctly completes the statement.
In the past four weeks, Jen earned a total income of $
1,031.20
562.00
312.00
281.20
31.20
Answers
Okay, here are the steps to solve this problem:
* Jen earns a weekly salary of $250
* She gets a 10% bonus on any sales
* In the past 4 weeks, she sold $312 worth of phones and accessories
* 10% of $312 is $31.20
* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80
* Her weekly salary is $250
* So in 4 weeks, her salary would be $250 * 4 = $1000
* Her total income over 4 weeks is $1000 + $124.80 = $1124.80
* The choices are:
** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20
So the correct choice is $1,031.20.
If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is
fo =
c + vo
c − vs
fs
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 32 m/s and accelerating at 1.1 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.5 m/s2, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)
Answers
Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.
It can be calculated as:
[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]
where:
c is the speed of light (c = 332m/s)
all the subscripted s is related to the Source (frequency, velocity);
all the subscripted o is related to the Observer (frequency, velocity);
As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.
So, the frequency perceived by the observer:
[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]
[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]
[tex]f_o=460(1.247)[/tex]
[tex]f_o= 573.6 \ \text{Hz}[/tex]
At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz
Answer:
The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time
The perceived frequency you hear is
370.9 Hertz
The function is given as:
[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x [tex]f_{s}[/tex]
From the question
[tex]c=332[/tex] --- speed of the sound
[tex]V_{o} =32[/tex] ---current speed of the train
[tex]V_{s} = 40[/tex] --- speed of the opposite train
[tex]f_{s} =460[/tex] --- frequency of the sound wave
This gives:
[tex]f_{o}= \frac{332-32}{332+40}[/tex] ×[tex]460[/tex]
[tex]f_{o}= \frac{300}{372} x460[/tex]
Rewrite as:
[tex]f_{o}= \frac{300x460}{372}[/tex]
[tex]f_{o}= 370.9[/tex]
traveled 1/5 miles in 3/2 hour. how many in 1 hour. show model fraction representation
Answers
a)Traveled 0.3 miles in 1 hour.
b) The fraction representation is 3/10 miles per hour.
a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.
Distance traveled = 1/5 miles
Time taken = 3/2 hours
To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:
3/2 = 15/10
Now we can divide the distance by the time:
1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15
This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).
To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):
2/15 x 10/3 = 2/9
Therefore, the person traveled 2/9 miles per hour.
b) To write this as a model fraction representation, we can express it as a single fraction:
2/9 = 3/10 (rounded to the nearest tenth)
So the person traveled at a rate of 3/10 miles per hour.
Lo learn more about fraction here
https://brainly.com/question/10354322
#SPJ1
Change 14,277 s to h, min, and s.
Answers
When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.
What is Conversion?Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.
How to determine this
When 60 seconds makes 1 minute
60 minutes makes 1 hour
14,277 seconds to minutes
When 60 seconds = 1 minute
14,277 seconds = x
x = 14,277/60 minutes
x = 237 minutes 7 seconds
By converting 237 minutes to hour
When 60 minutes = 1 hour
237 minutes = x
x = 237/60 hours
x = 3 hours 57 minutes.
Therefore, the conversion is 3 hours 57 minutes 7 seconds
Read more about Conversion
https://brainly.com/question/30765057
#SPJ1
What is the surface area of this cylinder?
Use 3.14 and round your answer to the
nearest hundredth.
2 ft
5 ft
square feet
Answers
The surface area of this cylinder is 942 millimeter square
How to determine the surface areaThe formula for the surface area of a cylinder is expressed as;
SA = 2πr h + 2πr²
Given that the parameters are identified as;
SA is the surface area of the cylinder.r is the radius of the cylinder..h is the height of the cylinderFrom the information given, we have that;
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 10²
Find the square values
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 100
Multiply the values
Surface area = 314 + 628
Now, add the values
Surface area = 942 mm²
Learn more about cylinders at: https://brainly.com/question/9554871
#SPJ1
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answers
Answer:
The correct equation is C. d = 163t.
This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).
Step-by-step explanation:
Which parent functions have a domain of all real values of x? Select all that apply.
A. Absolute value
B. Linear
C. Reciprocal
D. Quadratic
E. Cube root
F. Cubic
Answers
Answer:
D. Quadratic
Step-by-step explanation:
The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative
riangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
Answers
To find the scale factor used to dilate triangle ABC to triangle A'B'C', we need to compare the corresponding side lengths of the two triangles.
The distance formula can be used to find the lengths of the sides of triangle ABC:
AB = sqrt[(3 - (-3))^2 + (3 - (-3))^2] = sqrt[6^2 + 6^2] = 6sqrt(2)
AC = sqrt[(0 - (-3))^2 + (3 - (-3))^2] = sqrt[3^2 + 6^2] = 3sqrt(5)
BC = sqrt[(3 - 0)^2 + (3 - 3)^2] = 3
Similarly, we can use the distance formula to find the lengths of the sides of triangle A'B'C':
A'B' = sqrt[(9 - (-9))^2 + (9 - (-9))^2] = sqrt[18^2 + 18^2] = 18sqrt(2)
A'C' = sqrt[(0 - (-9))^2 + (9 - (-9))^2] = sqrt[9^2 + 18^2] = 9sqrt(5)
B'C' = sqrt[(9 - 0)^2 + (9 - 3)^2] = sqrt[9^2 + 6^2] = 3sqrt(5)
The scale factor is the ratio of the side lengths of the corresponding sides of the two triangles. For example, the scale factor for side AB is:
AB' / AB = (18sqrt(2)) / (6sqrt(2)) = 3
Similarly, we can find the scale factors for sides AC and BC:
A'C' / AC = (9sqrt(5)) / (3sqrt(5)) = 3
B'C' / BC = (3sqrt(5)) / 3 = sqrt(5)
Since the scale factors for all three pairs of corresponding sides are the same, the scale factor used to dilate triangle ABC to triangle A'B'C' is 3.
Therefore, the answer is 3.
I need help please I can’t figure this out
Answers
Answer: Area=3.125 square feet
Step-by-step explanation:
2.5x2.5=6.25
6.25/2= 3.125
Answer:
A = 50 ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
given that 1 inch equals 4 feet , then
b = 2.5 in = 2.5 × 4 feet = 10 feet
h = 2.5 in = 2.5 × 4 feet = 10 feet
then
A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²
The volume of blood in a person's body is proportional to body weight. A person who weighs 200 pounds has approximately 6 quarts of blood. Estimate the number of quarts of blood
in a person who weighs 90 pounds.
Complete the proportion, where the ratios have volumes of blood in the numerators and body weights in the denominators.
X
(Doshot simplify.)
X
More
Answers
The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.
How to calculate the number of quarts of blood the individual has?The body weight of the first individual = 200 pounds
The volume of blood = 6 quarts.
Therefore a person of 90 pounds = X quarts.
That is;
200 pounds = 6 quarts
90 pounds = X quarts
make X quarts the subject of formula;
X = 90×6/200
= 540/200
= 2.7 quarts
Learn more about volume here:
https://brainly.com/question/27710307
#SPJ1
The circle below has center O, and its radius is 5 m. Given that m LAOB = 30°, find the area of the shaded region and the length of the arc ADB. Give exact answers in terms of it, and be sure to include the correct units in your answer.
Answers
Measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and arc length ADB is 10.67π m
Given that the circle has a center O.
The radius of the circle is 8 m.
The measure of ∠AOB is 120°
We need to determine the area of the shaded region and the length of the arc ADB.
The measure of ∠ADB is given by
∠ADB = 360 - ∠AOB
= 360 - 120
=240 degrees
The area of the shaded region can be determined using the formula,
A = (θ/360) πr²
A = (θ/360) ×3.14× 8²
A = 42.67 m²
Thus, the area of the shaded region is 42.67π m²
The length of arc ADB can be determined using the formula,
Arc length = (θ/360) 2πr
=10.67π m
Hence, measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and length of arc ADB is 10.67π m
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ1
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Answers
Given
ABCΔ is a triangle.
D is a point on [BC]
|BD|=4
|AD|=|CD|
m(CBAˆ)=α=30∘
m(ACBˆ)=β=20∘
To Find
What is |AC|=x?
Solution
Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b
and applying law of cosines to all three triangles yields;
x=2acos20∘16=a2+b2+2abcos70∘(a+4)2=b2+x2+2bxcos50∘respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4
The complete question is -
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Learn more about from the given link
brainly.com/question/30239338
Which of the following is the expanded form of a number? Select all correct answers.
(A) 7·1000+8·100+3· 1/100
(B) 4·100+9·100+3· 1/10 +4· 1/10
(C) 71·10+4·1+6· 1/100 +5· 1/1000
(D) 5·1000+5·100+5·1+5·1/100
(E) 3·1000+8·1000+9·1/1000
(F) 9·1000+3·101+5· 1/10
Answers
(A) 7·1000+8·100+3· 1/100 is the expanded form of a number.
(B) 4·100+9·100+3· 1/10 +4· 1/10 is the expanded form of a number.
(C) 71·10+4·1+6· 1/100 +5· 1/1000 is the expanded form of a number.
(D) 5·1000+5·100+5·1+5·1/100 is the expanded form of a number.
(E) 3·1000+8·1000+9·1/1000 is the expanded form of a number.
(F) 9·1000+3·101+5· 1/10 is not the expanded form of a number as the second term 3·101 is not a valid place value.
Therefore, options A, B, C, D, and E are the correct answers.
Can someone actually help me with this!!!! please do A through D, I attached the picture. BRAINLIEST!!!!!
Answers
1. Substitute the smallest possible value for each variable into the inequality and check that the inequality is true.
2. Substitute the largest possible value for each variable into the inequality and check that the inequality is true.
3. Check that the solution set of the inequality contains only whole numbers, since the number of containers must be a whole number.
For example, let's check the compound inequality for the number of containers of cheese popcorn c:
5.65c + 0.4p ≤ 50 and c ≥ 0
1. Substituting c = 0 and p = 125 (the largest possible value) into the inequality, we get:
5.65(0) + 0.4(125) ≤ 50
50 ≤ 50
This is true.
2. Substituting c = 9 (the largest possible value) and p = 0 into the inequality, we get:
5.65(9) + 0.4(0) ≤ 50
50.85 ≤ 50
This is false.
3. The solution set of the inequality is:
0 ≤ c ≤ 8.849...
Since the number of containers must be a whole number, the solution set is:
0 ≤ c ≤ 8
Therefore, the compound inequality for the number of containers of cheese popcorn c is:
0 ≤ c ≤ 8
We can follow the same steps to check the compound inequality for the number of containers of peanut butter popcorn p.
A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?
Answers
To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
How long must the person leave the money in the bank until it reaches 20400 dollars?We can use the formula for compound interest:
A = P[tex](1 + r/n)^{nt}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.
Let's solve for t:
20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]
2.55 = [tex](1.00013)^{(365t)}[/tex]
Taking the natural logarithm of both sides, we get:
after solving
Using a calculator, we find:
t ≈ 15.5
So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
to know more about bank
brainly.com/question/14042269
#SPJ1
Find the sum of the interior angles of the following polygon:
115⁰
4
130⁰
115
95⁰
Sum of interior angles =
Part 2:
Find the measure of x:
degrees.
degrees.
Answers
The Sum of interior angles of the given polygon is: 540°
The value of the angle x is: 85°
What is the interior angle of the polygon?The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.
Sum of interior angles in a n-sided polygon is:
Sum = (n - 2)180
where:
n is the number of sides of the irregular polygon.
This is a 5-sided irregular polygon
Thus:
Sum = (5 - 2)180
Sum = 540°
Thus:
x + 115 + 115 + 130 + 95 = 540
x + 455 = 540
x = 540 - 455
x = 85°
Read more about Interior angle of Polygon at: https://brainly.com/question/224658
#SPJ1
Question 9 of 10
A rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
For what values of x are the two expressions equal?
O A. All real numbers except -4 and 2
OB. All real numbers except 2
C. All real numbers
D. All real numbers except -4
Answers
The values of x are the two expressions equal to All real numbers except 2.
We are given that rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.
The expression should be;
(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.
After simplification by (x - 2) , the remainder will be;
(x + 4)/9.
When x = -4, both sides equal to zero.
When x = 0 , both sides equal to 4/9
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
For each SSA case below, i) solve by the law of cosines, (ii) solve by the law of sines; use degrees for angles, and round each answer to its nearest 100th:
Answers
The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.
How to explain the angleSSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.
By sine rule,
Y = sin156.78 × 44 / 34
= 29
sin Y = 0.499
Y = 29.93°
By the angle sum property. The last angle will be:
180 - 156.78 - 29.93
= 6.67°
Learn more about triangles on
https://brainly.com/question/21629009
#SPJ1
Supplementary angles
Answers
Answer: ∠EGF and/or ∠CGB
Step-by-step explanation:
Starting Angle: ∠CGE
Possible Supplements: ∠EGF and ∠CGB
Find the measure of each indicated side. Round your answer to the nearest tenth.
Answers
Answer:
m∠R = 78.9°------------------------------
We are given three sides and need to find one of angles.
Use the law of cosines:
[tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]
Here we are given:
R - angle A, a = 59.7, b = 52, c = 41Substitute above values into the given equation:
[tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]
Find m∠R:
m∠R = arccos (0.1925), use calculatorm∠R = 78.9° (rounded to the nearest tenth)