We conclude that the width of the rectangular garden is 80 feet.
How to get the dimensions of the garden?Let's define the variables:
L = length of the garden.W = width of the garden.The perimeter of a rectangle of length L and width W is given by the simple formula:
P = 2*(L + W)
The perimeter is equal to 400ft, then:
400ft = 2*(L + W)
And we know that the length is 120ft, then:
L = 120ft.
Replacing the length in the perimeter equation we get:
400ft = 2*(120ft + W)
Now we can solve this linear equation for W.
400ft/2 = 120ft + W
200ft = 120ft + W
200ft - 120ft = W
80ft = W
We conclude that the width of the rectangular garden is 80 feet.
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Examine the diagram, where points B, C, D, and E lie on circle A. Angle BCD measures 57. PLS HELP
Answer:
BED =57°
Step-by-step explanation:
angle at circumference standing on the same arc
Please answer this question
Answer:
1 and 4
Step-by-step explanation:
x-1 = 0
x = 1
x^2 - 5x + 4
(x-4)(x-1) = 0
x can't be 1 or 4
Answer: 1 and 4
Step-by-step explanation:
1. To find excluded values, we need to make the denominator equal to zero.
x² - 5x + 4 = 0
2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:
(x - 4)(x - 1) = 0
x - 4 = 0 x - 1 = 0
x = 4 x = 1
These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.
one of the acute angles of a right triangle is 36° find the other acute angles
Step-by-step explanation:
An acute angle is an angle less or equal to 90 degrees.
let the other angle be x.
x + 36 = 90
grouping like terms
X = 90 - 36
X = 54 degrees
Answer:
54
Step-by-step explanation:
= ∠A + ∠B + ∠C = 180o … [∵sum of the angles of a triangle is 180]
or 180 = 36 + 90 + ∠C
C=54
TIME REMAINING
51:31
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(b) (x -10)(x +10)
Step-by-step explanation:
The factorization of the difference of squares is a special form:
a² -b² = (a -b)(a +b)
ApplicationYour expression is recognizable as the difference of squares:
x² -100 = x -10²
Using the above form, the factorization is ...
= (x -10)(x +10) . . . . . . . . matches the second choice
K
An employment agency specializing in temporary construction help pays heavy equipment operators $124 per day and general laborers $82 per day If thirty-seven people were hired
and the payroll was $3916, how many heavy equipment operators were employed? How many laborers?
The number of heavy equipment operators hired was?
The number of general laborers hired was?
Step-by-step explanation:
x = number of heavy equipment operators
y = number of general laborers
x + y = 37 (37 people were hired)
out if this we get e.g.
x = 37 - y
124x + 82y = 3916 (daily rate for each role, in total 3916)
now we use the first equation in the second :
124(37 - y) + 82y = 3916
4588 - 124y + 82y = 3916
672 - 42y = 0
672 = 42y
y = 16
x = 37 - y = 37 - 16 = 21
21 heavy equipment operators were hired.
16 general laborers were hired.
The length of a certain rectangle is 6 meters more than twice its width. What is the perimeter of the rectangle if the area of the rectangle is 260 square meters?
Answer:
Perimeter = 72 meters
Step-by-step explanation:
Let L be the length and W the width of the rectangle
We have the following relationship
L = 2W + 6
Area of the rectangle = LW = (2W+6)W by substituting for L
Area =
2W² + 6W =260 ==> 2W² + 6W -260 = 0
Dividing both sides by 2 yields
W² + 3W -130 = 0
This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation
However in this case it is easier to solve by factorization
W² + 3W -130
= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)
= (W+13)(W-10) = 0
This means W is either -13 or W = 10
Since W cannot be negative, we get W = 10 and
L = 2(10) + 6 = 26
Perimeter of a rectangle is given by
2(L + W) = 2(26 + 10) = 2(36) = 72 Answer
The scouts packed 9 boxes of different kinds of chips for their trip. Each box had 10 bags of chips. These clues show what they had left at the end of the trip. They ate all the rest.
Clues:
2 full boxes of potato chips and 3 bags left over
1 fewer box of nacho chips than potato chips, with no bags left over
twice as many loose bags of barbecue chips than loose bags of potato chips, with no full boxes left over
How many bags of chips did the scouts eat on their trip?
The scouts eat 51 bags of chips on their trip
How to determine the number of bags of chips?The given parameters are:
Boxes = 9
Bag = 10 chips
2 full boxes of potato chips and 3 bags left over.
This represents:
Potato chips = 2 * 10 + 3
Potato chips = 23 i.e. 23 bags potato chips are left over
1 fewer box of nacho chips than potato chips, with no bags left over
This represents
Nacho chips = (2 - 1) * 10
Nacho chips = 10 i.e. 10 bags of nacho chips are left over
The loose bags of potato chips is 3.
So, we have:
Barbecue chips = 2 * 3 bags
Barbecue chips = 6 bags
At this point, we have:
Potato chips = 23 bagsNacho chips = 10 bags Barbecue chips = 6 bagsThe total number of bags left over is
Total = 23 + 10 + 6
Total = 39
The number of bags eaten is:
Eaten = 9 * 10 - 39
Evaluate
Eaten = 51
Hence, the scouts eat 51 bags of chips on their trip
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AN ARTICLE IN USA TODAY STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND
ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15%
OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.
Step-by-step explanation:
I assume this means exactly one wrong number in the 10 attempts.
the probability to get a wrong number is 0.15 (15%).
therefore, the probability to get a correct number is
1 - 0.15 = 0.85
in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :
0.15×0.85⁹ = 0.034742542...
this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.
how many different constellations can we have that way ?
10.
because the wrong number could be given at any of the 10 attempts.
so, the probability to get exactly 1 wrong answer is
10×0.15×0.85⁹ = 0.34742542... ≈ 35%
now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.
the probability to get all 10 numbers correctly is
0.85¹⁰ = 0.196874404... ≈ 20%
and therefore, the probability to get at least 1 number wrong is
1 - 0.196874404... = 0.803125596... ≈ 80%
FYI :
this would be, of course, also the result of we did it the complex way :
the sum of the probabilities of
exactly 1 number wrong
exactly 2 numbers wrong
...
exactly 9 numbers wrong
all 10 numbers wrong
and for each of the cases of n wrong numbers the probability is
(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)
this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.
and again, all this summed up (1 <= n <= 10) is the same as
0.803125596...
The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Now, Let q = probability of giving out wrong number = 15 % = 0.15
And, p = probability of not giving out wrong number = 1 - q
= 1 - 0.15 = 0.75
Hence, For a binomial probability,
P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.
With n = 10 and x = 1, the probability of getting a number wrong
P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
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43. Which function has an x-intercept of 4?
A. f(x) =
= -√2x+4
B. f(x) = (x + 4)(x-7)
Soloct ono
C. f(x) = x² + 3x - 4
D. f(x)=x-4
Answer:
D
Step-by-step explanation:
When f(x) is equal to 0, x=4.
Consider an urn containing 8 white balls, 7 red balls and 5 black balls.
1)Randomly select 2 balls without replacement. The probability of getting 2 white balls is equal to:
2)Randomly select 5 balls without replacement. the probability of getting 2 white balls is equal to:
3) randomly select 150 balls with replacement. The probability of getting at least 72 white balls is:
Answer + Step-by-step explanation:
1) The probability of getting 2 white balls is equal to:
[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]
2) the probability of getting 2 white balls is equal to:
[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]
3) The probability of getting at least 72 white balls is:
[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]
[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]
First of all, we would determine the total number of balls in the urn as follows:
Total number of balls = 8 + 7 + 5
Total number of balls = 20 balls.
Next, we would determine the probability of getting two (2) white balls without replacement:
P(2 white balls) = 8/20 × 7/19
P(2 white balls) = 2/5 × 7/19
P(2 white balls) = 0.1474.
Part 2.When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:
P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]
P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = 0.3456.
Part 3.When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Substituting the given parameters into the formula, we have;
P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]
P = 0.7948.
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Which of the following inequalities represents the number line below?
Answer:
x ≤ 4
Step-by-step explanation:
the solid dot at 4 indicates that x can equal 4
the arrow points to the left indicating values less than 4 , then
x ≤ 4
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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PLease see attached. This is an algebra question
The solution for the given expression is 16.
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
First, you apply the Power Rules - Power for [tex](\frac{2^2x^2y}{xy^3} )^2}[/tex]. For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:[tex]\frac{16x^4y^2}{x^2y^6}[/tex].
After that, you should apply the Power Rules - Division . For this rule, you should repeat the base and subctract the exponents. Thus, the result will be:[tex]\frac{16x^2}{y^4}[/tex].
Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:[tex]\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16[/tex]
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The world price of umbrellas is $20 each. The pre-trade price of baskets in England is S15 each. What would happen if England allows trade in baskets?
Answer: Ans. Option c As the price of basket in England is $15, which is less than the world
integer for 1,440 feet below sea level
If you borrow $100 for 5 years at an annual interest rate of 8%, how much will you pay all together
Answer:
$140
Step-by-step explanation:
interest = 8x5 = 40
total = time + interest
total = 100 + 40 = $140
why kilogram is more appropriate unit than milligram?
Step-by-step explanation:
that question is fundamentally wrong.
"appropriate" completely depends on the situation and circumstances.
if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.
if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".
because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.
if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.
Calculate the weight on earth of an object with a mass of 48kg
Answer: 470.4 N
Step-by-step explanation:
Concept:
1 kg on Earth = 9.8 N
Given information:
Mass = 48 kg
Find the weight on Earth
1 kg = 9.8 N
48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
Solve using the distributive property -5(-3u-3x+4)
Answer:
15u+15x-20
Step-by-step explanation:
* = multiply or times
We have to multiply everything in the parenthesis by -5, meaning:
-5*-3u = 15u
-5*-3x = 15x
-5*4 = -20
Put it all together: 15u+15x-20
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the distributive formula?}[/tex]
[tex]\mathsf{a(b + c)}\\\\\mathsf{= a(b) + a(c)}\\\\\mathsf{= ab + ac}[/tex]
[tex]\large\textbf{Extended distributive property formula:}[/tex]
[tex]\mathsf{a(b + c + d)}\\\\\mathsf{= a(b) + a(c) + a(d)}\\\\\mathsf{= ab + ac + ad}[/tex]
[tex]\huge\textbf{What are we solving for?}[/tex]
[tex]\large\textbf{It seems like you have the extended distributive property}[/tex]
[tex]\mathsf{-5(-3u - 3x + 4)}[/tex]
[tex]\huge\textbf{What are the steps to solving for the}\\\\\huge\textbf{given equation?}[/tex]
[tex]\mathsf{-5(-3u - 3x + 4)}\\\\\mathsf{= -5(-3u) - 5(-3x) - 5(4)}\\\\\mathsf{= 15u + 15x - 20}[/tex]
[tex]\huge\textbf{What is the answer to the equation?}[/tex]
[tex]\huge\boxed{\frak{{= 15\mathsf{u} + 15\mathsf{x} - 20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically, the formula for calculating probability is expressed as:
Probability = expected outcome/Total outcome
Sample space is the total number of element in a given set of probability. The subsets if this sets are called event
Let the six children the couple plan to have ne 1, 2, 3, 4, 5,6 such that the sample space will be:
S = {1, 2, 3, 4, 5, 6}
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
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The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a
The best sampling strategy would be a stratified sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.
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What is the least common multiple of 6x^2+39x-21 and 6x^2+54x+84?
12x² + 102x² + 114x - 84
Answer:
Solution Given:
1st term: 6x²+39x-21
Taking common
3(2x²+13x-7)
doing middle term factorization
3(2x²+14x-x-7)
3(2x(x+7)-1(x+7))
3(x+7)(2x-1)
2nd term: 6x²+54x+84
taking common
6(x²+9x+14)
doing middle term factorization
6(x²+7x+2x+14)
6(x(x+7)+2(x+7))
2*3(x+7)(x+2)
Now
Least common multiple = 2*3(x+7)(2x-1)(x+2)
2(x+2)(6x²+39x-21)
(2x+4)(6x²+39x-21)
2x(6x²+39x-21)+4(6x² + 39x-21)
12x³+78x² - 42x+4(6x² + 39x-21)
12x³+78x² - 42x + 24x² + 156x-84
12x³ + 102x²-42x + 156x - 84
12x² + 102x² + 114x - 84
Answer:
[tex]12x^3+102x^2+114x-84[/tex]
Step-by-step explanation:
Given polynomials:
[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]
Factor the polynomials:
Polynomial 1
[tex]\implies 6x^2+39x-21[/tex]
[tex]\implies 3(2x^2+13x-7)[/tex]
[tex]\implies 3(2x^2+14x-x-7)[/tex]
[tex]\implies 3[2x(x+7)-1(x+7)][/tex]
[tex]\implies 3(2x-1)(x+7)[/tex]
Polynomial 2
[tex]\implies 6x^2+54x+84[/tex]
[tex]\implies 6(x^2+9x+14)[/tex]
[tex]\implies 6(x^2+7x+2x+14)[/tex]
[tex]\implies 6[x(x+7)+2(x+7)][/tex]
[tex]\implies 6(x+2)(x+7)[/tex]
[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]
The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.
Therefore, the LCM of the two polynomials is:
[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]
[tex]\implies (6x^2+54x+84)(2x-1)[/tex]
[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]
[tex]\implies 12x^3+102x^2+114x-84[/tex]
A large university has 24,000 students. A
randomly selected sample of 750 students
were surveyed and asked how far away
they live from the university. Of those
surveyed, 120 students live more than
500 miles away from the university.
Based on the survey results, estimate the
number of students who live within 500
miles of the university?
Answer:
23370 students live with in 500 miles of the university.
Step-by-step explanation:
large university students =24000
selected students = 750
surveyed students =120 lives far away from university.
students live with in 500mile=?
750-120=630
24000-630=23370
What is 3/2+ t = 1/2
Answer:
t=-1Step-by-step explanation:
To find the value of t, isolate it on one side of the equation.
[tex]\sf{\dfrac{3}{2}+t=\dfrac{1}{2}}[/tex]
First, you subtract by 3/2 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{3}{2}+t-\dfrac{3}{2}=\dfrac{1}{2}-\dfrac{3}{2}}[/tex]
Solve.
1/2-3/2
1-3/2
1-3=-2
-2/2
Divide.
-2/2=-1
[tex]\Longrightarrow: \boxed{\sf{t=-1}}[/tex]
Therefore, the solution is t=-1, which is our answer.
I hope this helps, let me know if you have any questions.
STEP BY STEP EXPLANATION;
1.To solve the equation,the least common multiple of the denominators must be found.
LCM=2
Therefore,
3/2 +t =1/2
2.Each term must be multiplied by the LCM.
i.e
2(3/2)+2(t)=2(1/2)
3+2t=1
2t=1-3 ( subtracting 3 from each side of the equation)
2t=1-3
2t/2=-2/2 (dividing both sides of the equation by the co-efficient of t)
t=-1
A positive integer is 10 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(2,3), then find the two integers.
The two integers are are mathematically given as
x=3.70
y=13.7
What is the two integers?Generally, the equation for the two integers is mathematically given as
x + 10 = y
1/x + 2/y = 2/3
Substitute
1/x + 2/x+10 = 2/3
Multiply by 3
3/x + 6/x + 10 = 2
Multiply by x
2 + 6x/x + 10 = 2x
Multiply by x + 3
2(x + 10) + 6x = 2x(x + 3)
2x+20+6x=2x^2+6x
-2x^2+2x+20=0
x=3.70
hence y
x + 10 = y
3.70+ 10 = y
y=13.7
In conclusion, the two integers are
x=3.70
y=13.7
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The volume of a sphere is 4500π m3. What is the surface area of the sphere to the nearest square meter?
Answer:
2827 m²
Step-by-step explanation:
The equation for volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Using this equation and the given volume of the sphere, we can find the radius of the sphere.
Finding the Radius[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]4500\pi = \frac{4}{3}\pi r^3[/tex]
Divide both sides by π
[tex]4500=\frac{4}{3}(r^3)[/tex]
Multiply both sides by 3
[tex]13500=4( r^3)[/tex]
Divide both sides by 4
[tex]3375=r^3[/tex]
Take the cube root of both sides
[tex]r=15[/tex]
Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.
Finding the Surface AreaThe equation for surface area of a sphere is [tex]4\pi r^2[/tex]. Substituting the value we found for the radius into the equation, we find:
[tex]SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2[/tex]
The surface area of the sphere, rounded to the nearest square meter, is 2827 m².
Question 5
Find the interest rate for a principal of $6570 and charged $30105 in interest for 12 years.
The Formula is
I
PT
x 100
Take the interest divide by the principal
then divide by the years
then times by 100
Round your answer to 1 decimal place.
Answer:
R=i
Step-by-step explanation:
R=i×100÷p×t
r=30105×100÷6570×12
r=3010500÷78840
r=38.18
PLS HELP
Which functions have a range of {y e R-00 < y < 00}?
O f(x)
2x+3
Of(x) = x - 8
O f(x) = x² + 7x - 9
O f(x) = -4x + 11
O f(x) = -(x + 1)² - 4
=
Answer:
[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]
Step-by-step explanation:
- Range is a set of all y-values in a set of coordinate points.
A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.
An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:
Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.
For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:
Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.
The length and width of a rectangle is 42cm and 28cm respectively. The ratio between the two
quantities is ____________.
Answer:
The ratio is 3 : 2.
Step-by-step explanation:
42 cm : 28 cm
= 21 : 14 (Divide both sides by 2)
= 3 : 2 (Divide both sides by 7)
The ratio between the length and width of the rectangle is 3:2.
We have,
The concept used here is the concept of ratio.
In mathematics, a ratio is a comparison of two quantities.
It expresses how many times one quantity contains another or how many times it is greater or smaller than the other quantity.
The ratio between the length and width of the rectangle can be found by dividing the length by the width:
Ratio = Length / Width
= 42 cm / 28 cm
= 7 x 6 / 7 x 4
Cancel out the common factor.
= 6/4
= 2 x 3 / 2 x 2
Cancel out the common factor.
= 3/2
Thus,
The ratio between the length and width of the rectangle is 3:2.
Learn more about ratios here:
https://brainly.com/question/2462048
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