Jack's problems illustrates algebraic expressions
He solved m/5 problems everyday.75 questions were assigned in totalNumber of problems solved per dayThe given parameters are:
Problems = mNumber of days = 5The number of questions solved per day is calculated as:
Daily = Days/Problems
So, we have:
Daily = m/5
Number of problems in the assignmentWe have:
Daily = m/5
He solved 15 daily.
So, the equation becomes
m/5 = 15
Multiply both sides by 15
m = 75
Hence, 75 questions were assigned in total
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2. When an adult is physically active, suppose the amount of water they will consume is normally distributed with an average of 20 ounces of water with a standard deviation of 7 ounces. If 10 adults are physically active, what is the probability that the average water consumed by them is less than 18 ounces? (note that we are working with a sampling distribution in this question). Report to 5 decimal positions
Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].
For samples of n = 10, the standard error is given by:
[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]
The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 20}{2.2136}[/tex]
Z = -0.9.
Z = -0.9 has a p-value of 0.18406.
0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
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Find the value of the expression 1/2x + 3 if x = 12
Step-by-step explanation:
please mark me as brainlest
Factor each completely.one zero has been given
f(x)=x^3-4x+16;-2
F(x) = X^4+ 2x^-13x^2 -10x + 40;2
F(x)=x^3-3x^2-13x+15;-3
F(x)=x^4-8x^3+19x^2-12x;3
The polynomials in factored form are listed below:
f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716) f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)f(x) = (x + 3) · (x - 5) · (x - 1)f(x) = (x - 4) · (x - 3) · (x - 1) · xHow to factor polynomialsIn this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:
[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex] (1)
Where:
[tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient[tex]r_{i}[/tex] - [tex]i[/tex]-th RootRegarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])f(x) = (x + 3) · (x - 5) · (x - 1)
Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
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A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
Answer the Both (a) and (b) . And show the method too. I will make Brainelist + 50 points
#a
4p-6pq+9q-64p-3(2pq+3q-2)#b
That be x and y
So
x+y=15--(1)2x+4y=64--(2)So
from eq(1)
x=15-y--(3)Put in second one
2(15-y)+4y=6430-2y+4y=642y=34y=17Put in third one
x=15-17x=-2Take it positive
x=2Answer:
(a) (i) Factorize [tex]\sf 4p-6pq+9q-6[/tex]
Rewrite by swapping the order of the first two terms:
⇒ -6pq + 4p + 9q - 6
Factorize the first two terms and the last two terms separately:
⇒ -2p(3q - 2) + 3(3q - 2)
Factor out the common term (3q - 2):
⇒ (3q - 2)(-2p + 3)
(ii)
Square of the binomial: [tex](a+b)^2=a^2+2ab+b^2[/tex]
Rewrite [tex]9.9[/tex] as [tex]10 - 0.1[/tex]
Therefore, [tex]a = 10[/tex] and [tex]b = -0.1[/tex]
Also, remember that multiplying a number by 0.1 is the same as dividing it by 10. (when dividing a decimal number by 10, simply move the decimal point 1 place to the left).
[tex]\begin{aligned}\implies 9.9^2 & =(10-0.1)^2\\ & =10^2-2 \cdot 10 \cdot 0.1+0.1^2\\& = 100-\dfrac{2 \cdot 10}{10}+\dfrac{0.1}{10}\\& =100-2+0.01\\ & =98 + 0.01\\ & = 98.01\end{aligned}[/tex]
(b) (i)
Let x = number of motor bicycles
Let y = number of cars
Given:
There are 15 vehicles of two types⇒ x + y = 15
Given:
The number of tires in all vehicles is 64⇒ 2x + 4y = 64
(ii) Rewrite x + y = 15 to make x the subject:
⇒ x = 15 - y
Substitute into 2x + 4y = 64 and solve for y:
⇒ 2(15 - y) + 4y = 64
⇒ 30 - 2y + 4y = 64
⇒ 30 + 2y = 64
⇒ 2y = 34
⇒ y = 17 cars
Substitute found value of y into x = 15 - y to find x:
⇒ x = 15 - 17 = -2 motorbikes
**There must be an error in the question, as with the given information, the number of motorbikes is -2, which is impossible.**
Here are the possible combinations of number of motorbikes (M) and number of cars (C) whose sum of tires is 64. As you can see, there is no combination that sums to 15 vehicles:
0 M + 16 C = 16 vehicles
2 M + 15 C = 17 vehicles
4 M + 14 C = 18 vehicles
6 M + 13 C = 19 vehicles
8 M + 12 C = 20 vehicles
10 M + 11 C = 21 vehicles
12 M + 10 C = 22 vehicles
14 M + 9 C = 23 vehicles
16 M + 8 C = 24 vehicles
18 M + 7 C = 25 vehicles
20 M + 6 C = 26 vehicles
22 M + 5 C = 27 vehicles
24 M + 4 C = 28 vehicles
26 M + 3 C = 29 vehicles
28 M + 2 C = 30 vehicles
30 M + 1 C = 31 vehicles
32 M + 0 C = 32 vehicles
These numbers are multiples of __________.
4, 8, 16, 24
A) 3
B) 4
C) 5
D) 6
Answer:
4
Step-by-step explanation:
All these numbers multiply by 4
Answer:
The answer is B.
Step-by-step explanation:
4÷4=1
8÷4=2
16÷4=4
24÷4=6
The coldest temperature recorded on the surface of a planet was - 248 Celsius is the warmest temperature recorded on the surface of the planet was 108 Celsius what are the correspondence temperatures in degrees Fahrenheit
Answer:
-414.4 F° and 226.4 F°
hope it helps
The volume of a right cone is 252pi units^3. If its height is 21 units, find its radius.
Based on the calculations, the radius of this right cone is equal to 6 units.
Given the following data:
Volume of cone = [tex]252\pi \;units^3[/tex]Height of cone = 21 units.How to calculate the volume of a cone.Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Making r the subject of formula, we have:
[tex]r=\sqrt{\frac{3V}{\pi h} } \\\\[/tex]
Substituting the given parameters into the formula, we have;
[tex]r=\sqrt{\frac{3\times 252\pi}{\pi \times 21} } \\\\r=\sqrt{\frac{756}{21} }\\\\r=\sqrt{36}[/tex]
r = 6 units.
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Consider the rectangle with width 4 ft and length 18 ft, write a ratio of the length to the width.
Answer: 18:4
Step-by-step explanation:
Ez
Answer:
9 : 2
Step-by-step explanation:
length : Width = 18 : 4
[tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]
= 9 : 2
Choose the correct graph of the function y=√x-3
Answer:
C. where the start point is on (3,0) and goes up and to the right
Step-by-step explanation:
y= √x−3
Swap sides so that all variable terms are on the left hand side.
√x−3 =y
Square both sides of the equation.
x−3=y^2
Add 3 to both sides of the equation.
x−3−(−3)=y^2 −(−3)
Subtracting −3 from itself leaves 0.
x=y^2 −(−3)
Subtract −3 from y^2.
x=y^2 +3
I need the answer to this quick pls
Answer:
Option A
Step-by-step explanation:
The median of the trapezoid is the line connecting the midpoints of the legs.The median of the trapezoid can be caculated by the fromula,
[tex]\bf Median = \dfrac{a +b}{2}[/tex]
Here, a and b are the base (parallel sides)
a = 13 inches & b = 19 inches
[tex]\bf Median = \dfrac{13+19}{2}[/tex]
[tex]= \dfrac{32}{2}\\\\\\= 16 \ inches[/tex]
* PLEASE HELP ME SOLVE THIS PROBLEM I WILL GIVE BRAINIEST*
2. Change from dog/cat to tails/heads.
DDC = ________
CDC= _________
DCD = ________
CCD = _________
DDD = _________
CCC = _________
DCC = _________
CDD = _________
please help :))
Answer:
Tails Tails Heads
Heads Tails Heads
Tails Heads Tails
Heads Heads Tails
Tails Tails Tails
Heads Heads Heads
Tails Tails heads
Heads Tails Tails
------------------------------------------------——------------------------------------------------------
Thanks!
Always keep more than 2 smiles so that you can share it to someone who doesn't have one. You happy! Me happy! EVERYONE HAPPY!!!!
Have a great day!
:D
How do I solve it the problem completely
Answer:
42 in²
Step-by-step explanation:
Total: Shape 1 + Shape 2
Area of a square: l x w, where l is the length and w is the width.
= 6 x 5
= 30
Area of a triangle: 1/2 x b x h, where b is the base and h is the height.
= 1/2 x 4 x 6
= 1/2 x 24
= 12
Total = 30 + 12
= 42 in²
Answer:
Step-by-step explanation:
This figure is trapezium
a and b are the parallel lines.
a = 5 +4 = 9 in & b = 5 in and h = 6 in
[tex]\boxed{\text{Area of trapezium =$\dfrac{(a+b)*h}{2}$}}[/tex]
[tex]\sf = \dfrac{(9+5)*6}{2}\\\\=\dfrac{14*6}{2}\\\\= 7*6\\\\= 42 \ in^{2}[/tex]
If 10% of your paycheck was withheld for federal income taxes and another 6% for state income taxes, how much would your net (or take-home) pay be?
Your net income/take-home would be 84.6 percent of the gross amount.
What is net income?Your net income is the amount of money left after payroll deductions in the form of taxes and other charges on the gross amount of your paycheck.
If we deduct federal and state taxes, 10 percent and 6 percent respectively, we would charge 10 percent and 6 percent of 100 and have 84.6 percent of your original(gross) income left.
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For each pair of real numbers show that the first number is a factor of the second number?
Need help ASAP!!
Answer:
[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]
Answer:
Putanginaaaaaaaaaaaaaaaaaaaaa
A car dealership sold 212 cars in 4 months. At what rate did the dealership sell cars in cars per month?
Answer: 59 cars per month
Step-by-step explanation:
Is ABSE- ATES? If so, identify the similarity postulate or theorem that
applies.
Find the value of the expression 1/2x+3 if x=12
Answer:
The answer is 9.
Step-by-step explanation:
1/2 * 12 = 6
6+3=9
Answer:
9
Step-by-step explanation:
x = 12
1/2 · 12 = 6
6 + 3 = 9
Find the greatest possible number of consecutive zeros at the end of the product of three positive integers if the sum of these three integers equals 939.
Answer:
I think its 5 consecutive zeros.
Step-by-step explanation:
This would be a guess but I think you would need two numbers in the hundreds that also have 2 parts of which have a product of a number ending in 0, like 4 and 5.
So my guess would be
400 * 500 * 39
= 7800000
Express √12+√27 in the form n√3, where n is an integer.
Answer:
5sqroot3
Step-by-step explanation:
see image.
An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.
To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image
Which is the inverse of the function f(x) = 4x − 9?
Step-by-step explanation:
x and y trade places.
f(x) = y = 4x - 9
y + 9 = 4x
x = (y + 9)/4
and to make it a true function notation, we need to rename x to y and vice versa and get
y = (x + 9)/4
Jessica sells 50.5 ounces of lemonade for a total of 20.20.
Find the unit price in dollars per ounce.
If necessary, round your answer to the nearest cent.
Answer:
2.5
Step-by-step explanation:
Answer: 2.5
Step-by-step explanation: do it yourself jk lol first you add then divide by 6.5
What is the product?
48+ 2 K-2
24 2+1
4
O2k+1
2
K-2
2
2641
2
R+2
Answer:
[tex]\frac{2}{k+2}[/tex]
Step-by-step explanation:
Simplify the expression and you will get this.
hope this helps
how many one third cup servings are in 16 cups
Gabrielle’s age is two time Mikhaïl’s age. The sum of their ages is 27. What is Mikhail’s age?
Mikhail is 9
Step-by-step explanation:
Divide 27 by 3 because G is 2 times than Mik. So G=2 Mik=1. and 27 divided 3 is 9
[tex] \rm \int_{0}^2 \left( \sqrt[3]{ {x}^{2} + 2x} + \sqrt{1 + {x}^3 } \right )dx \\ [/tex]
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]
Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:
[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]
and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].
So, we can write the given integral as
[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]
Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get
[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
A 34
B 47.5
C 68
D 95
Answer:
A
Step-by-step explanation:
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
What does using the degrees of freedom in a sample correct for? possible bias between the alternative and null hypotheses possible bias between the sample and the population possible bias between the standard deviation and variance possible bias between the standard deviation and the mean
In Statistics and mathematics, the degrees of freedom in a sample are used to correct: A. possible bias between the alternative and null hypotheses.
What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined as the opposite of an alternate hypothesis ([tex]H_a[/tex]), and it asserts that two (2) possibilities are the same.
In In Statistics and mathematics, the test statistics of a given sample is calculated with this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the sample size.Also, the degrees of freedom in a sample are used to correct a possible bias that exists between the alternative and null hypotheses.
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A group of people are fundraising, and each person raises a certain amount of money for every mile they walk. Each person's fundraising is represented below using d for the dollars that person raises and w for the miles that person walks. Select all the representations that can be described by the equation d = 2w.
Answer:
B, C, EStep-by-step explanation:
According to coordinates on the graphs and numbers in the tables we have the following relationship:
A) d = 1/2wB) d = 2wC) d = 2wD) d is not proportional with w since 12/6 ≠ 18/10 ≠ 20/12E) d = 2wAs we see B, C and E have same relationship, matching the target.
Step-by-step explanation:
hope it's help you this answer
The length is :____meters and the width is____meters.
Answer:
Length = 42, Width = 14
Step-by-step explanation:
Say width = x
3x + x = 56
4x = 56
x = 14
14 x 3 = 42.
Answer:
width = 7
length = 21
Step-by-step explanation:
x + 3x = 56/2
4x = 28
x = 7