side 1 = x
side 2 = x+5
side 3 = x+14
perimeter = side 1 + side 2 + side 3
133 = x + (x+5) + (x +14)
133=3x + 19
114=3x
x=114/3 = 38
side 1 = 38
side 2 = x+5 = 38+5 = 43
side 3 = x+14 = 38+14 = 52
38+43+52 = 133
side lengths are 38, 43 & 52
What is the eighth term of the geometric sequence 4,-20,100,...?
The eighth term of the geometric sequence 4, -20, 100,... is 9600, calculated using the formula aₙ = arⁿ⁻¹ with a = 4, r = -5, and n = 8.
The eighth term of the geometric sequence 4, -20, 100,... is 9600.
To find the eighth term of a geometric sequence, you can use the formula: aₙ = arⁿ⁻¹, where a is the first term, r is the common ratio, and n is the term number. In this case, a = 4, r = -5, and n = 8.
Plug the values into the formula: 4 x (-5)⁸⁻¹ = 9600.
Miguel earns $490 a week, and he works 5 days a week. What is his daily wage?
Answer: $98 per day
Step-by-step explanation:
Let us calculate the amount he is paid per day.
Since Miguel works 5 days a week, we will divide his total pay per week by the number of days he works every week to get the amount of money he is paid daily.
Therefore, daily pay = 490/5
daily pay =$ 98.
Alternatively,
If 5 days ------> $490
1 day------->$x
Cross multiply and work out the value of x:
5x = 490
therefore, x= 490/5
x=$98 /day
what is the least common multiple of 20 and 52
The least common multiple of 20 and 52 is, 420
What is Least common multiple?The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 20 and 52
Now, The factors of numbers are,
⇒ 20 = 2 × 2 × 5
⇒ 42 = 2 × 3 × 7
Hence, The least common multiple of 20 and 52 is,
⇒ LCM of {20, 52} = 2 × 2 × 5 × 3 × 7
= 420
Thus, The least common multiple of 20 and 52 is, 420
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1/2 of a group of chickens tried to cross the road. Only 3/4 of those chickens made it to the other side. What fraction of the original group of chickens made it to the other side?
Answer:
[tex]\frac{3}{8}[/tex] of the group
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] of a group of chickens tried to cross the road.
only [tex]\frac{3}{4}[/tex] of those chickens made it to the other side.
So [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{3}{8}[/tex] of the group of chickens made it to the other side.
Find the amount of time to the nearest day it would take a deposit of $1300 to grow to 1 million at 17% compounded continuously. The amount of time it would take to grow the deposit to $1 million is____ years ___ days
It would take approximately 39 years and 183 days for the deposit to grow to $1 million.
Use the concept of compound interest defined as:
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given that,
Initial deposit: $1300
Target amount: $1 million
Interest rate: 17%
Compounding: Continuous
Time to calculate: To the nearest day
To find the amount of time it would take,
Use the formula:
[tex]t = \dfrac{ln(\frac{M}{P})}{r}[/tex]
Where,
t = time in years
M = final amount ($1 million)
P = initial deposit ($1300)
r = interest rate (17% or 0.17)
Find the natural logarithm of the ratio M/P:
ln(1,000,000 / 1,300) ≈ 6.64
Divide the result by the interest rate:
t = 6.64 / 0.17
t ≈ 39.05 years
So, it would take approximately 39 years to grow the deposit to $1 million.
To determine the number of days,
Multiply the decimal part of the years by 365 (assuming a non-leap year):
0.05 x 365 ≈ 183 days
Hence,
Rounding to the nearest day, it would take approximately 39 years and 183 days for the deposit to grow to $1 million.
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The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8
A figure with 5-part symmetry has 5 lines of symmetry.
Explanation:A figure with 5-part symmetry has 5 lines of symmetry. This means that it can be divided into five equal parts by rotating it around these lines. Each line of symmetry divides the figure into two mirror-image halves.
Which is least? 0.105 0.501 0.015 or 0.15
The lowest decimal number from 0.105, 0.501, 0.015, and 0.15 is 0.015. This is because when we compare the numbers from left to right, 0.015 has the smallest digit (0) at the second decimal place which is the hundredths place.
Explanation:To determine which decimal number is the lowest, it's helpful to compare these numbers digit by digit from the left. The four numbers are 0.105, 0.501, 0.015, and 0.15. Each of them starts with 0. The second digit of 0.105, 0.501, and 0.15 is 1, but the second digit for 0.015 is 0. So, 0.015 is the lowest number because it has the smallest digit (0) in the second decimal place (hundredths place). Remember, these numbers are read as decimals and not as whole numbers, so the digit at each decimal place has a different significance.
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Six years from today you need $10,000. you plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays an 8% effective annual rate. your last deposit, which will occur at the end of year 6, will be for less than $1,500 if less is needed to reach $10,000. how large will your last payment be?
Amount of last payment is approximately $497
Given that;
Number of year = 6 year
Annual deposit = $1,500
Annual rate = 8% = 0.08
Find:
Amount of last payment
Computation:
[tex]Future\ value = Annual\ deposit[(1+r)^n - 1]/r[/tex]
[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[\frac{(1+0.08)^6 - 1}{0.08}][/tex]
[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[(1.08)^6 - 1]/0.08\\\\Future value of the 6 annual deposits = 1500[0.58687]/0.08[/tex]
Future value of the 6 annual deposits = 11,003.25
Future value of the 6 annual deposits = $11,003 (Approx.)
Extra payment = 11,003 - 10,000
Extra payment = $1,003
So,
Amount of last payment = 1,500-1,003
Amount of last payment = $497
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Would you measure walls using inches or yards
81.54 is what percent of 75.5
Find the number of interest periods required to achieve the conditions set forth. A = $5,000 P = $2,000 interest is 5% compounded semiannually
Rewrite sin 15 degree in terms of a 75 degree angle and in terms of the reciprocal of a trigonometric function.
which number is a factor of 20, but not a multiple of 2? 12, 5, 10 or 4?
if the GCF of two numbers is 1, they are called relatively prime. Find three sets of relatively prime numbers
The GCF can be obtained by taking the prime factors of two numbers then multiplying the common prime factors. IF there are none, then the GCF is 1 and the numbers are called relatively prime.
There are a lot of relatively prime numbers. To name three sets:
3 and 19
7 and 20
15 and 28
For these sets, we see that there are no other common factors except 1. To illustrate the factors:
3 = 1, 3
19 = 1, 19
7 = 1, 7
20 = 1, 2, 2, 5
15 = 1, 3, 5
28 = 1, 2, 2, 7
So we see that only the number 1 is the factor in each set.
Final answer:
Three sets of relatively prime numbers are 9 and 16, 14 and 25, and 8 and 21, as they do not share any common prime factors other than 1.
Explanation:
If the Greatest Common Factor (GCF) of two numbers is 1, they are indeed referred to as relatively prime. To find sets of relatively prime numbers, we need to identify pairs of numbers that do not have any prime factors in common other than 1.
9 and 16: The prime factors of 9 are 3· 3, and the prime factors of 16 are 2· 2· 2· 2. They share no common prime factors, so they are relatively prime.
14 and 25: The prime factors of 14 are 2· 7, and the prime factors of 25 are 5· 5. Since they have no common factors, these numbers are also relatively prime.
8 and 21: The prime factors of 8 are 2· 2· 2, and the prime factors of 21 are 3· 7. With no prime factors in common, 8 and 21 are relatively prime.
Therefore, we have found three sets of relatively prime numbers: 9 and 16, 14 and 25, and 8 and 21.
The surface areas of two similar solids are 340 yd2 and 1,158 yd2. The volume of the larger solid is 1,712 yd3. What is the volume of the smaller solid?
Let us say that,
1 = smaller solid
2 = larger solid
We must remember that the surface area of an object is proportional to the square of their sides, therefore,
SA = k s^2
where k is the constant of proportionality.
By taking the ratio of the 2 similar solids:
SA2 / SA1 = k s2^2 / k s1^2
SA2 / SA1 = s2^2 / s1^2
sqrt (SA2 / SA1) = s2 / s1
s2 / s1 = sqrt (1158 / 340)
While the volume of an object is proportional to the cube of
their sides, therefore:
V = k’ s^3
where k’ is the constant of proportionality.
By taking the ratio of the 2 similar solids:
V2 / V1 = k’ s2^3/ k’ s1^3
V2 / V1 = s2^3/ s1^3
1712 / V1 = [sqrt (1158 / 340)]^3
1712/V1 = 6.28556705
V1 = 272.37 yd^3
A DELL computer hardware has a yearly 17% rate of failure. Answer the following question. Convert your answer to a percentage. What is the probability that if you buy four computers, at least 1 will fail within a year?
Answer:
Failure of a Single Dell computer in terms of percentage=17%
It means you buy a computer, there is 17% chance that it will be bad Machine and (100-17)%=83% chance that, it will be a good machine.
Probability that if you buy four computers, atleast 1 will fail within a year
[tex]=_{1}^{4}\textrm{P}\times [P(S)]^3\times P(F)+_{2}^{4}\textrm{P}\times [P(S)]^2\times [P(F)]^2+_{3}^{4}\textrm{P}\times P(S)\times [P(F)]^3+_{4}^{4}\textrm{P}\times [P(F)]^4\\\\=4 \times (0.83)^3\times (0.17)+6\times (0.83)^2\times (0.17)^2+4\times (0.83)\times (0.17)^3+1\times (0.17)^4\\\\=0.3881516+0.11945526+0.01631116+0.00083521\\\\=0.52475323[/tex]
=0.53(Approx)
=0.53 × 100
=53%
4.4 mi/h how many ft/s
Answer:
about 6.45 ft/s
Step-by-step explanation:
The conversion factor for mph to fps is ...
1 mph = 22/15 fps
Multiplying by 4.4 gives ...
4.4 mph = 96.8/15 fps = 484/75 fps = 6 34/75 fps
≈ 6.4533333... ft per second
(1 point) suppose that the trace of a 2×22×2 matrix aa is tr(a)=−4tr(a)=−4, and the determinant is det(a)=0det(a)=0. find the eigenvalues of aa.
There are 9 more pencils then pens in a container. There are 25 writing utensils in the container in all. How many pens are there in the container?
the slope of a line is 2/3. what is the slope of a line that is perpendicular to this line? Type a numerical answer in the space provided. do not include spaces in your answer. if necessary, use the / key to represent a fraction bar and only type improper fractions (no mixed numbers).
Two parallel lines are crossed by a transversal. What is the value of x?
A. x = 12
B. x = 14
C. x = 22
D. x = 24
Answer
x = 12
Explanation
The two given angles are supplementary angles. That means that the add up to 180 degrees.
(5x + 5) + 115 = 180
5x +5 + 115 = 180
5x + 120 = 180
5x= 180 - 120
5x = 60
x = 12
can someone pls answer
9y = -11x +36
y = -11/9 +4
y = 4
A league of 19 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)
A Way to write numbers by using the digits 0-9, with each digit havin a place value
______ ?
Your six month old baby has doubled his birth weight, is grasping objects and pulling them to his mouth, and seems hungry all the time despite the eight full bottles he drinks each day. do you start solids yet
I would say that the child is prepared for solid foods because it is capable of grasping things such as food. If the baby can gulp easily and sit up without adjustment solids are okay to switch the child on at this point. Also you can give a child solid food anywhere starting from 4-6 months old.
Supplementary breast milk is given to babies after babies 6 months of age and over with a gradual texture starting from fine, filtered porridge, pureed porridge, then solid food such as adult food. Complementary food for breast milk is better if it contains 4 stars namely carbohydrates, vegetable protein, animal protein, and vegetables.
Further Explanation
When a baby enters the age of 6 months, he needs more calories than just the nutrition he gets through exclusive breastfeeding. At this age, you can introduce your baby's first solid food.
Feeding is not just filling the baby's stomach with nutritious food, but also provides education about pleasant interactions, stimulation of the sense of taste, fine motor training (moving hands and directing to the mouth that requires good coordination between hands, eyes, and of course, the brain), chewing and discipline.
8 Solid Foods for 6-Month-Old Babies
Cereal Banana Sweet Potato Avocado Chicken or Beef Meat Pear Tofu Wheat bread
In addition to some of the foods above, introduce other solid foods as well. Of course, the texture must be adjusted to the stage of growth of the baby. Do not forget, introduce food one by one to see what foods cause allergies in children.
In general, the purpose of first feeding for babies from 6 months of age are:
Meet the nutritional needs of babies. Develops the baby's ability to accept a variety of foods with different tastes and textures. Develops and trains baby's motor skills such as chewing and swallowing.
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Details
Grade: College
Subject: Health
Keyword: complementary, food, baby
The equation y = ax describes the graph of a line. If the valise of a is positive , the line:
32x - 4 = 4x2 + 60 For the equation shown, choose the description of the solutions.
Final answer:
The quadratic equation 32x - 4 = 4x2 + 60 has real and equal solutions after rearranging to 4x2 - 32x + 64 = 0 and recognizing it as a perfect square.
Explanation:
To solve the equation 32x - 4 = 4x2 + 60, we first rearrange it into standard quadratic form ax2 + bx + c = 0.
We move all terms to one side: 4x2 - 32x + 64 = 0. Once in this form, we can use the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a), or factor if it is factorable, to find the solutions for x. After rearranging, we note that the quadratic is a perfect square, giving us (2x - 8)2 = 0, which means that the solution for x is 4, with multiplicity of two since it is a repeated root.
The description of the solutions would be that they are real and equal, since we have a repeated solution.
The Canadian $1 coin has a diameter of 26.5 mm.what is the circumference of the coin?use 3.14 for pie
circumference = diameter x PI
26.5*3.14 = 83.21 mm
Answer: 83.21 mm
Step-by-step explanation:
The circumference of a circle is given by :-
[tex]\text{Circumference }=\pi d[/tex]
Given : The Canadian $1 coin has a diameter of 26.5 mm.
Then , the circumference of the coin will be :-
[tex]\text{Circumference of coin}=\pi (26.5)=(3.14)(26.5)\\\\\Rightarrow\text{Circumference of coin}=83.21\text{ mm}[/tex]
Hence, the circumference of the coin is 83.21 mm
How is inductive reasoning used in geometry?
Answer:
Inductive reasoning draws general conclusions from specific details / observations - in other words, going from specific --> general.
Example:
Specific: I break out when I eat peanuts.
Observation: This is a symptom of being allergic.
General Conclusion: I am allergic to peanuts.
hope this helps! <3
Final answer:
Inductive reasoning in geometry involves observing patterns in specific instances and formulating general rules or hypotheses, such as the sum of angles in a triangle or the properties of parallel lines intersected by a transversal.
Explanation:
Inductive reasoning in geometry is used to derive broad generalizations from specific observations or instances. One way inductive reasoning is applied is by observing patterns or properties in a set of geometric figures and then formulating a hypothesis or general rule that applies to all similar figures. For example, after measuring the angles of several triangles and finding that they always add up to 180 degrees, one might assume that all triangles have this property. Another example is when looking at multiple parallel lines cut by a transversal and noticing the corresponding angles are equal, thus generalizing that this is the case for any parallel lines intersected by a transversal.
Scientists, including mathematicians, use inductive reasoning to construct hypotheses, which are then tested using deductive reasoning. The conclusions drawn from inductive reasoning may not always be correct, but they are essential for advancing scientific and mathematical knowledge by suggesting relationships and rules that can be rigorously tested.
A furniture store is having a going-out-of-business sale. Two hours after opening, there are 415 sofas still available. Three hours later, there are 301 sofas available. How many hours will the store have to stay open to sell the entire inventory? Assume the sales rate is constant and round your answer to the nearest whole hour.