c= 4√7
1) Given that we have a leg of 12 and a hypotenuse of 16 units. Let's use the Pythagorean Theorem to find the missing leg.
2) a² =b²+c²
hypotenuse² = leg² +leg²
16² =12² +c²
256= 144 + c²
256 -144 = c²
112=c²
√c²=√112
c=4√7 (approximately 10.58 units)
3) Hence, we can state that the missing leg has the size of 4√7 units
On her first day in a hospital, Kiri receives u, milligrams (mg) of a therapeutic drug. The amountof the drug Kiri receives increases by the same amount, d, each day. On the seventh day,she receives 21 mg of the drug, and on the eleventh day she receives 29 mg.(a)Write down an equation, in terms of u, and d, for the amount of the drug that she receives(0)on the seventh day;
Answer
The equation for the amount of drug received on the 7th day in terms of u and d is
a₇ = u + 6d
Explanation
The description of the amount of drug administered on the first day and how the amount increases each day by d shows that this is an arithmetic progression question.
For an arithmetic progression with first term, u, and common difference, d, the nth term is given as
aₙ = u + (n - 1) d
a) So, for the 7th day
a₇ = u + (7 - 1) d
a₇ = u + 6d
Hope this Helps!!!
y = 2x + 1y = -x - 2Solve the following system by graphing. What isthe solution?1. (-1, -3)2. (-1, 3)3. (-1, -1)4. (3, -1)
75 1/3% as a fraction in the simplest form
226/3 %
hope this helped
Answer:
The answer for this is 226/3%
Which proportion would use to find the area of the sector given the below figure
Explanation
From the question, we are given that
[tex]\begin{gathered} \bar{AC}=radius(r)=7 \\ \angle C=\theta=80^0 \end{gathered}[/tex]If the area of a sector is denoted by x, recall that its formula can be expressed as;
[tex]\begin{gathered} x=\frac{\theta}{360}\times\pi r^2 \\ \therefore\frac{\theta}{360}=\frac{x}{\pi r^2} \end{gathered}[/tex]We can then substitute the parameters into the above formula.
[tex]\begin{gathered} \frac{80}{360}=\frac{x}{\pi7^2} \\ \Rightarrow\frac{80}{360}=\frac{x}{49\pi^{}} \end{gathered}[/tex]Answer:
[tex]\frac{80}{360}=\frac{x}{49\pi^{}}[/tex]How do i write 4/5inch per hour as a ratio
Answer:
4/5 to 1
Step-by-step explanation:
you just put the numbers next to each other
Answer:
4 : 5 are 8 : 10 and 12 : 15
Step-by-step explanation:
Therefore, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15. Note: In this question we can't apply division method to get the answer in integer form because the G.C.F. of 4 and 5 is 1. That means, 4 and 5 cannot be divisible by any other number except 1.
4. Sampling students A statistics class with 30 students has 10 varsity athletes and 20 who are not. Choose 2 of th students in the class at random. Find the probability that both are not varsity athletes. a. Draw a tree diagram to model this chance process.
A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The probability that the 2 students chosen are not varsity athletes is 38/87
What is a combination?It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
Number of students = 30
Number of varsity athletes = 10
Number of non-varsity athletes = 20
Number of students chosen at random = 2
The probability that the 2 students chosen are not varsity athletes:
= [tex]\frac{^{20}C_2}{^{30}C_2}[/tex]
= 10 x 19 / 15 x 29
= 2 x 19 / 3 x 29
= 38 / 87
Thus,
The probability that the 2 students chosen are not varsity athletes is 38/87
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Hana is organizing a 3/4 mile fun run. There will be a water station every 1/4 of a mile after the start. How many water station will there be?
There will be 3 water stations along the fun run using the mathematical operation of division.
What is a mathematical operation?A mathematical operation uses addition, subtraction, division, or multiplication to reach a result after combining variables, numbers, and mathematical operands.
In this situation, we only use division to get the quotient, which is the number of water stations along the fun run.
The total distance for a fun run = 3/5 miles (0.75 miles)
The spread of the water station along a mile = every 1/4 mile (0.25 miles)
The number of water stations along the run = 3 (0.75/0.25)
Thus, Hana needs to station 3 water stations along the run by dividing the total distance by the expected spread.
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help me decide wheter this is SSS, SAS, or AA problemsI choose SAS, am I right?
Yes, they are similar triangles.
The answer is SSS
Given a 10 sided figure how many diagonals can you draw from one vertex?
the scale model of a rectangular garden is 1.5 ft by 4 ft. the scale model is enlarged by a scale factor of seven to create the actual garden period what is the area of the actual garden?6 ft squared42 ft squared252 fr squared294 ft squared
Answer
Option D is correct.
294 ft squared
Explanation
The scale model of the rectangular garden is 1.5 ft. by 4 ft.
The model is then enlarged by a scale factor of 7 to create the actual garden.
So, we can now find the length of the actual garden
The Length of the actual garden = 4 × 7 = 28 ft.
The Width of the actual garden = 1.5 × 7 = 10.5 ft.
The area of a rectangle is given as
Area = Length × Width
= 28 × 10.5
= 294 ft squared
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I will show you the pic
to determine the product between the 2 numbers we must write both numbers in scientific notation
[tex]800.5=8.005\cdot10^2[/tex]now we multiply both number without the tenth potency.
[tex]8.005\cdot2=16.01[/tex]now we add the tenth potencies
[tex]\begin{gathered} 16.01\cdot10^{6+2} \\ 16.01\cdot10^8 \end{gathered}[/tex]now we move 1 decimal place more to the left to make the number between 0 and 9.9
[tex]16.01\cdot10^8=1.601\cdot10^9[/tex]When Trina arrived to take her driving test, there was a 193 minute wait. If she has waited 88 minutes so far, how much longer does she have to wait to take her test?
Tina has to wait 105 minutes more before she can take the test.
What is subtraction?
Subtraction is one of the basic arithmetic operation which means minus or difference between two or more values.
We are given that when Trina arrive for the test she has to wait 193 minutes before she could take the test
Now she has waited 88 minutes so far
We have to subtract this two values to find how long she has to wait before she could take the test.
Therefore we get,
[tex]193-88=105[/tex]
Hence She has to wait 105 minutes before she could take the test.
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30 year term calculation
In 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.
What is a loan amortization schedule?It is defined as the systematic way of representing of loan payments according to the time in which the principal amount and interest are mentioned in a list manner
It is given that:
P = 63,000
i = 5.3%
t = 30 years
[tex]\rm Total \ amount = P\times\dfrac{(\dfrac{r}{n})(1 + r/n)^{tn}}{(1 + r/n)^{tn}-1}[/tex]
After putting the values in the formula we get:
Total amount = $1,259,430.95
Thus, in 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.
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KX
KY
GIVEN PROBLEM
F
Problem 1: Solving Equations with Variables on Both Sides!
Given the equation 5x + 1 = 3x + 5, order the steps
below to correctly solve for x.
5x-3x=5-1
2x=2
x=1
Step-by-step explanation:
make the xes one side and the numb one side first and solve:
Answer: Step by Step Explanation Step 1: take 3x to the right side of equals to whereas 1 to the left side of it i.e. 5x-3x=5-1
Step2: Apply arithmetic operations now, it comes as 2x=4
Step3: Now x will stay at the left side, 1 goes to the divide 4 i.e. X=4/2 which equals to 2
Answer
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches, and standard deviation of 9.4 inches.
The probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.
As per the question statement, in the country of United States, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches and standard deviation of 9.4 inches. We are supposed to find the probability that a randomly chosen child has a height of less than 33.3 inches.
z = (X - μ) / σ, where X is the data data, μ = mean, σ = standard deviation
z = (66.09 - 56.8) / 9.4
z = 0.988 or 98%
So, the probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about probability, click on the link given below:
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Nathan is planning to ride his bike for 24 minutes. Write an equation that Nathan can use to find d, the distance he will travel in 24 minutes, if his rate in miles per hours is represented by r
Answer:
Step-by-step explanation:
We are required to find the distance Nathan will travel.
Total distance travelled of Nathan is 2 miles
speed = Total distance travelled ÷ Total time take
total distance travelled = Speed × Total time taken.
Speed = 5 miles per hour
Time = 24 minutes
Convert minutes to hour
60 minutes = 1 hour
24 minutes = 0.4 hour
total distance travelled = Speed × Total time taken
= 5 miles per hour × 0.4 hour
= 2 miles
Therefore, total distance travelled of Nathan is 2 miles
Use the equation of the polynomial function f(x)=−2x3−x to complete the following.(a) State the degree and the leading coefficient.(b) Describe the end behavior of the graph of the function.(c) Support your answer by graphing the function.
The function given is,
[tex]f(x)=-2x^3-x[/tex](a)We need to find the degree and leading coefficient of the function.
The degree is the highest power of the polynomial.
We can see that it is a cubic polynomial, or, a third degree function.
The leading coefficient is the coefficient of the highest degree term.
In our case, -2 is the leading coefficient because it is the coefficient of x^3.
(b)The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
Let's graph the function:
From the graph, we can see,
• As x approaches infinity, the function approaches negative infinity
,• As x approaches negative infinity, the function approaches positive infinity
This describes the end behavior of the function.
(c)From our function graphed above, we see that "D", from the answer choices, represents the correct graph of this function.
Answer(s)(a)The degree of the polynomial is 3 and the leading coefficient is - 2.
(b)The curve opens down to the right because the leading coefficient is negative. Because the polynomial is cubic, the graph has end behaviors in the opposite direction, so the other end opens up to the left.
(c)D
Nick had $100 in his savings account.over the next 6 months, he worked at a seasonal store, where each month he earned $400 and spent $250.He put the remaining amount in his savings account each month.Now that the job is over, he plans to spend $200 per month. For how many months can he
Make withdrawals from his savings account until his balance is $0
After the 6 months of work he has $1000 on the account, and with that, he can spend $200 each month for 5 months.
For how many months can he make withdrawls?
We know that Nick initially had $100 on his savings account.
Then each month (for 6 months) he earns $400 and spends $250 and puts the rest in the savings account, the rest will be:
$400 - $250 = $150
If he saves this for 6 months, then he adds:
6*$150 = $900
And he already had $100 on the account, so now he has a total of:
$900 + $100 = $1000
For how many months can he take $200 of the account?
To see that, we need to take the quotient between the total amount and what he takes each month:
$100/$200 = 5
5 months.
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Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene’s car had 6.5 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cos $3.70 per gallon.
How much did Irene spend on gas?
After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
What are mathematical operations?An operation is a mathematical function that converts zero or more input values into an output value with a known value.The number of operands affects how complex the operation is.The order of operations refers to the rules that define the sequence in which multiple operations should be performed to solve an expression.PEMDAS is an abbreviation for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the amount Irene spends on gas:
The gas in the tank is 6.5 gallons.The gas amount per gallon is $3.70.Then, the amount of 6.5 gallons of gas:
6.5 × 3.70 = $24.05Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
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Find the solution(s) for x in the equation below. 12 + 10.1 + 21 = 0 O A. I = -3; I = -7 OB. I = -3; 1 -3; r = 7 O c. 3; 1 = -7 3; D = 7 OD..I
Answer:
Choice A: x = -3, x = -7
Explanation:
To solve the equation for x, we use the quadratic formula which says that if you have an equation
The monthly service charge $S of mobile phone is the sum of two parts. One part is a constant and the other varies directly as the connection time t minutes. When the monthly service charge is $230, the connection time is 100 minutes. When the monthly service charge is $290, the connection time is 130 minutes.a) Express S in terms of t.b) Find the value of the connection time t when the monthly service charge$S is $330.
Since the monthly charge S is made from 2 parts,
A constant part, let it b
A part depends on a direct relationship between it and the time t
Then the form of S should be
[tex]S=mt+b[/tex]Where:
m is the rate of change
b is the constant amount
Since S = 230 at t = 100
Since S = 290 at t = 130
Substitute them in the equation above to make 2 equations of m, b and solve them
[tex]\begin{gathered} 230=100m+b\rightarrow(1) \\ 290=130m+b\rightarrow(2) \end{gathered}[/tex]Subtract equation(1) from equation (2) to eliminate b
[tex]\begin{gathered} (290-230)=(130m-100m)+(b-b) \\ 60=30m \end{gathered}[/tex]Divide both sides by 30 to find m
[tex]\begin{gathered} \frac{60}{30}=\frac{30m}{30} \\ 2=m \\ m=2 \end{gathered}[/tex]Substitute m in equation (1) by 2 to find b
[tex]\begin{gathered} 230=100(2)+b \\ 230=200+b \end{gathered}[/tex]Subtract both sides by 200
[tex]\begin{gathered} 230-200=200-200+b \\ 30=b \\ b=3 \end{gathered}[/tex]a) The equation of S is (substitute m by 2 and b by 30)
[tex]S=2t+30[/tex]b) Since the monthly fee is $330, then
S = 330
Substitute it in the equation to find t
[tex]330=2t+30[/tex]Subtract 30 from both sides
[tex]\begin{gathered} 330-30=2t+30-30 \\ 300=2t \end{gathered}[/tex]Divide both sides by 2 to find t
[tex]\begin{gathered} \frac{300}{2}=\frac{2t}{2} \\ 150=t \\ t=150 \end{gathered}[/tex]The value of the time is 150 minutes
Hannah reads at a constant rate of
3pages every 8minutes.
Write an equation that shows the relationship between
p, the number of pages she reads, and
m
mm, the number of minutes she spends reading.
The relationship between p, the number of pages she reads, and m, the number of minutes she spends reading is 8p = 3m.
It is given in the question that Hannah reads at a constant rate of 3 pages every 8 minutes.
We have to write an equation that represents the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading.
If she reads 3 pages every 8 minutes, then
She reads 1 page every 8/3 minutes.
If she reads p pages , she will take 8p/3 minutes
If m represents the number of minutes she she spends reading p pages.
Then, we can write,
8p/3 = m
8p = 3m
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single letter from the word ALFALFA is chosen. What is the probability of choosing an For an A? Express your answer as a fraction in owest terms or a decimal rounded to the nearest millionth
ANSWER
5/7
EXPLANATION
The word ALFALFA has 7 letters, of which there are:
• 3 A
,• 2 L
,• 2 F
If we choose a single letter, the probability of choosing an F is,
[tex]P(F)=\frac{2}{7}[/tex]And the probability of choosing an A is,
[tex]P(A)=\frac{3}{7}[/tex]Since we are choosing a single letter, there is no event where we can choose both an F and an A at the same time, so the probability of choosing an F or an A is,
[tex]P(F\text{ }or\text{ }A)=P(F)+P(A)=\frac{2}{7}+\frac{3}{7}=\frac{5}{7}[/tex]Hence, the probability of choosing an F or an A is 5/7.
In a study of pain relievers, 20 people were given Product A, and all but 4 experienced relief. In the same study, 50 people were given Product B, and all but 6
experienced relief.
Fill in the blanks below to make the statement the most reasonable possible.
Product (choose one) performed worse in the study because % failed to get relief with this product, whereas only % falled to get relief
with Product (choose one)
The correct answer is Product (B) performed worse in the study because 90% failed to get relief with this product, whereas only 20% failed to get relief with Product (A).
How to solve study based problems?
In mathematics, the study based problems are analyzed with the given percentage data. The calculation is based on statistical result and comparison results.
According to the question, the detailed study of pain relievers states that the 20 people were given Product A, and all but 4 experienced relief. And in the same study, 50 people were given Product B, and all but 6 experienced relief.
Let us assume total number of people be 100.
For the Product B, only 6 people got the relief that means out of 100 people only 12 got the relief which means Product B is performed worst.
Similarly, for the Product A, only 4 people got relief that means out of 100 people almost 20 people got the relief which means it is better than the product B.
Hence, the correct answer is Product (B) performed worse in the study because 90% failed to get relief with this product, whereas only 20% failed to get relief with Product (A).
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help me please
thank you
Answer:
Domain: [1, 7], Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Hey does anyone mind helping me and explaining? I would Appreciate it!
Photo is attached
Answer:
A
Step-by-step explanation:
Corresponding sides of similar figures are in proportion.
A purple paint requires a proportional
relationship of number of quarts of red paint, r,
to blue paint, b. This is represented by the
equation.
3r = 24b
Enter the number of quarts of red paint used
for one quart of blue paint. (1 pt)
The number of quarts of red paint used for one quart of blue paint is 0.125 quarts.
Given that:
A purple paint requires a proportional relationship of number of quarts of red paint, r, to blue paint, b. This is represented by the equation 3r = 24b.
3r = 24b
b = 3r/24
b = r/8
b = 0.125r
So 0.125 quarts of red paint used for one quart of blue paint.
Hence the number of quarts of red paint used for one quart of blue paint is 0.125 quarts.
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Match the function to the table of values 2. 7. yurt 3 8. y=r-7 9. y=x+2 I 10. = 3+1
If you use the values of the table for each of the equations, you can find the answers
find the absolute value |97| =
Absolute value means take the non-negative number of what is between the bars
|97|
Since 97 is already positive, the absolute value of 97 is 97
The highest temperature recorded in the town of Westgate this summer was 95°F. Lastwinter, the lowest temperature recorded was -5°F. Find the difference between theseextremes.
Given:
The highest temperature is 95° F.
Lowest temperature is -5° F.
The difference between these temperature is,
[tex]95^{\circ}-(-5^{\circ})=95^{\circ}+5^{\circ}=100^{\circ}[/tex]Answer: The between the temperature is 100° F.
