Using the z-distribution, the 95% confidence interval for the proportion is given as follows:
(0.4576, 0.5824).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters for the interval are given as follows:
[tex]n = 246, \pi = 0.52[/tex].
The lower and upper bound of the interval, respectively, are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]
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What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
O If x is not even, then x + 1 is not odd.
O If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
OIf x is even, then x + 1 is not odd.
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The correct answer is If x + 1 is odd, then x is even.
What is the converse of the conditional?A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The conditional statement is known as p q in geometry. q p is how people refer to the Converse.One can obtain the contrary assertion by switching "p" and "q locations "in the condition. An example of a condition is "If Cliff is thirsty, then she drinks water." If Cliff drinks water, then she is thirsty, is the converse of the first sentence.The four primary varieties of conditional phrases are Zero Conditional, First Conditional, Second Conditional, and Third Conditional.The converses of the conditional statement:
"If q then p" provides the converse statement to the conditional expression "If p then q."
The converse of the conditional statement is If x + 1 is odd, then x is even.
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Look for a pattern in the data set to determine which kind of model best describes the data.
Running Speed of a Human
Distance Traveled
(miles)
1
2
3
4
Average Speed
(miles per hour)
7
6.3
5.67
5.103
The data appear to be linear.
The data appear to be quadratic.
The data appear to be cubic.
The data appear to be exponential.
On looking for a pattern in the given data set, the quadratic model best describes the data.
2nd option is correct.
A data model represents the type of relationship between the variables of a data set.
Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.
Given data is:
Distance Traveled Average Speed(miles per hour)
(miles)
1 7
2 6.3
3 5.67
4 5.103
A quadratic model is the best data model for the given data set.
The pattern observed in the given data set observes the properties of a quadratic function.
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Answer:
Exponential is the correct answer.
Step-by-step explanation:
If the hypotenuse is c=a√2, then 6=a√2. In inches, what is the value of a?
The value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2. This can be obtained by using Pythagoras' theorem.
Calculate the value of a:This question can be solved using Pythagoras' theorem,
If in a right angled triangle, hypotenuse is the longest side of the triangle and always opposite to the angle 90°, height and base are the two shorter sides which are adjacent to the angle 90°.
If hypotenuse = c, height = a and base = b then,
⇒ hypotenuse² = height² + base²
⇒ c² = a² + b²
Here in the question it is given that,
Hypotenuse of the triangle is c = a√2 6 = a√2 in inches ⇒ c = 6 Height and base is equal and both has the value of a ⇒ height = a and base = aBy using the Pythagoras' theorem we can write that,
⇒ hypotenuse² = height² + base²
⇒ 6² = a² + a²
⇒ 36 = 2a²
By dividing both sides of the equation by 2,
⇒ 18 = a²
⇒ a² = 18
By taking square on both side of the equation,
⇒ a = 3√2 inches
Hence the value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2.
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Find the value of x.
answer choices
A. 70
B. 65
C. 30
D. 40
The value of x is 70°. The correct option is A. 70
Circle GeometryFrom the question, we are to determine the value of the measure of arc x
From one of the circle theorems, we have that
The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.
First, we will determine the value of the third angle in the triangle formed.
Let the angle be y
y + 15° + 20° = 180°
∴ y = 180° - 15° - 20°
y = 145°
Now, the angle supplementary to this is the angle the arc subtends at the circumference.
Thus,
The angle at the circumference = 180° - 145°
The angle at the circumference = 35°
From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°
∴ The measure of the arc is 70°
This is the value of x
Hence, the value of x is 70°. The correct option is A. 70
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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.
the number has 3 digits the number is less than 140 the number has 7 as a factor the number is even the sum of the digits is less than 9
Answer:
It could be 105, 112 or 133.
Step-by-step explanation:
Having 7 as a factor means it is a multiple of 7.
The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105
Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133
→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.
The sum of the digits of these number is:
105 → 1 + 0 + 5 = 6
112 → 1 + 1 + 2 = 4
119 → 1 + 1 + 9 = 11
126 → 1 + 2 + 6 = 9
133 → 1 + 3 + 3 = 7
Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.
a chord subtend an angle of 72⁰ at the center of a circle with radius 24.5m. calculate the perimeter of the minor segment
The perimeter of the minor segment is 77. 4m
How to determine the perimeter
The formula for determining the perimeter of the minor segment is given as;
Perimeter = θ/360 × 2πr + 2r sin θ/2
where;
radius = 24. 5mθ = 72Substitute into the formula;
Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)
Perimeter = 30. 79 + 46. 60
Perimeter = 77. 4 m
Thus, the perimeter of the minor segment is 77. 4m
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A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find: d for t=3.5
1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. the distance travelled at time t = 3.5 h is 18 Km
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
1. How to determine the formula expressing the dependence of the variable s on tFrom the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.
Thus, we shall determine the distance travel in time t as follow
Speed = 12 Km/hTime = tDistance in time t = ?Speed = distance / time
12 = distance / t
Cross multiply
Distance = 12 × t
Distance in time t = 12t
But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:
s = 60 - 12t
Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. How to determine the distance at t = 3.5 hoursThe distance at t = 3.5 hours can be obtained as illustrated below:
Time (t) = 3.5 hoursDistance (s) = ?s = 60 - 12t
s = 60 - (12 × 3.5)
s = 60 - 42
s = 18 Km
Thus, the distance travelled at t = 3.5 hours is 18 km
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need heeeelp please
Answer:
please how
Step-by-step explanation:
I will help ypu
PLEASE HELP ASAP PLEASE PLEASE
Answer:
transitive property
Step-by-step explanation:
This is the answer by definition.
The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.
In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.
According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."
According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.
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A textbook store sold a combined total of 204 math and psychology textbooks in a week. The number of math textbooks sold was three times the number of psychology textbooks sold. How many textbooks of each type were sold?
A total of 204 textbooks were sold with 153 math textbooks and 51 psychology textbooks being sold, as the number of math textbooks was three times the number of psychology textbooks.
Given that,
The combined total of math and psychology textbooks sold in a week is 204.
The number of math textbooks sold is three times the number of psychology textbooks sold.
To solve this problem,
Assign variables to represent the number of math and psychology textbooks sold.
Let's say "M" represents the number of math textbooks and "P" represents the number of psychology textbooks.
We know that the combined total of math and psychology textbooks sold is 204,
So the equation be:
M + P = 204 .....(i)
We are also given that the number of math textbooks sold was three times the number of psychology textbooks sold.
In equation form, this can be expressed as:
M = 3P
Now, we can substitute the value of M in terms of P into the equation (i):
3P + P = 204
Combining like terms, we get:
4P = 204
Dividing both sides by 4, we find:
P = 51
So, the number of psychology textbooks sold is 51.
To find the number of math textbooks sold,
Substitute this value back into the equation:
M = 3P
M = 3(51)
M = 153
Therefore, the number of math textbooks sold is 153.
Hence,
153 math textbooks and 51 psychology textbooks were sold.
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Distribute to create an equivalent expression with the fewest symbols possible.
7(4p + 2q + 3r) =7(4p+2q+3r)
The equivalent expression for the given expression is 28p + 14q + 21r.
What is an equivalent expression?An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.
An equivalent expression is simplified to the original expression by using the distributive property.
What is distributive property?The distributive property is
a(b + c) = ab + ac
Calculation:The given expression is 7(4p + 2q + 3r)
Applying the distributive property,
7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)
⇒ 28p + 14q + 21r
Thus, the equivalent expression for the given expression is 28p + 14q + 21r.
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7(4p+2q+3r)=7(4p+2q+3r)
Apply distributive law
a(b+c)=ab+acSo
28p+14q+21r=28p+14q+21rThis is the required expression
1. a) Sajina deposited Rs 20,000 at the rate of 8% p.a. in her saving account. After 2 years, she withdrew Rs 5,000 and the total interest of 2 years. How long should she keep the remaining amount to get total interest of Rs 6,800 from the beginning?
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
What is meant by total interest?Total interest is the sum of all interest payments made during the course of an account or loan, including compounded amounts on accumulated interest that has not yet been paid.The equation [Total Loan Amount] = [Principle] + [Interest Paid] + [Interest on Unpaid Interest] can be used to calculate it.Under Section 24, you may deduct up to Rs 2 lakh from your total income for the interest component of the EMI you paid during the year.
How long should she keep the remaining amount to get a total interest of Rs 6,800 from the beginning:
The rate of 8% p.a. in her saving account.
20,000 at 8% interest for 2 years:
= 20,000*2*8/100
= 3200
5000 was withdrawn after 2 years and earned interest.
After 2 years, the new principal:
= 20000- 5000
=15000
She needs to get interested of 6800–3200 =3600 for the next N years.
N= 100* I /PR
= 100*3600/(15000*8)
=3
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
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Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
What is the formula for total interest?For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].
Given that Sajina deposited Rs 20,000 at the rate of 8% p.a. in her savings account.
So, [tex]P=20,000[/tex] and [tex]r=8[/tex].
Thus, after t=2 years the total interest would be
[tex]I=\dfrac{Prt}{100}\\\Longrightarrow I=\dfrac{20000\times 8\times 2}{100}\\\therefore I=3200[/tex]
So, the total interest after 2 years would be Rs 3,200.
Given that Sajina withdrew Rs 5,000 and the total interest of 2 years.
So, the new principal will be [tex]P'=20,000-5,000=\test{Rs}\hspace{1mm}15,000[/tex].
The total interest she wanted to gain is Rs 6,800. She had already gained Rs 3,200.
so, the remaining interest [tex]I'=6,800-3,200=\text{Rs}\hspace{1mm}3,600[/tex].
Let the required time be [tex]t'[/tex] years after how many years she got a total interest of Rs 6,800 from the beginning.
For principal [tex]P'=15,000[/tex], rate of interest [tex]r=8\%[/tex]; the total interest after [tex]t'[/tex] years would be [tex]I'=\dfrac{P'rt'}{100}=\dfrac{15000\times 8\times t'}{100}=1200t'[/tex]. But given that [tex]I'=3600[/tex].
So, we must have
[tex]1200t'=3600\\\Longrightarrow t'=\dfrac{3600}{1200}\\\therefore t'=3[/tex]
Therefore, Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
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In the circle below, O is the center and mGl= 145°. What is the measure of the central angle ZGOR? H G 0 145° I
The measure of the central angle is 290 degrees
How to determine the measure of the central angle?The measure of arc GI is given as:
mGI = 145 degrees
The measure of the central angle is calculated as:
Central angle = 2 * mGI
Substitute the known values in the above equation
Central angle = 2 * 145
Evaluate the product
Central angle = 290
Hence, the measure of the central angle is 290 degrees
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PLEASE HELP ME WITH THIS PROBLEM!!!
Answer: Moderate negative association
Step-by-step explanation:
a negative association or in other terms correlation, suggests that while one variable increases the other decreases and vice versawhen looking at the graph, the data shows a negative correlationas the x variable increases the y variable decreasesthis not a perfect correlation as the the change in value of variable x is not directly proportional to the change in value of yUse the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given the polynomial:
-2x³ - 7x² + 3x - 4
Simplifying:
= -(2x² - x + 1)(x + 4)
Hence:
-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)
(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
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The legs of a right triangle measure 3 cm and 8 cm. What is the length of the hypotenuse?
plesee help me do I need it under 25min and don't answer if you don't know or else u will be reported thank you (◔‿◔)
Answer:
l = 2.25 cm
Step-by-step explanation:
given l is inversely proportional to w² then the equation relating them is
l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion
(i)
to find k use the condition w = 1.5 , l = 16 , then
16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )
36 = k
l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion
(ii)
when w = 4 , then
l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm
. Which of the following statements is not true?
a. If x = 1, then x² = 1.
b. If x²= 1, then x = 1.
c. If x=-1, then x² = 1.
d. x² = 1.if and only if x = 1 or x = -1.
Answer:
If x^2 = 1, then x = 1 is NOT true because x can also be -1.
In questions 6 – 9, state the solutions for the quadratic equation depicted in the graph.
Step-by-step explanation:
It is just where it crosses the x axis
6) -3, -4
7) 1, -6
8) -5, -6
9) 3, -2.5
If k and b are constant such that lim x approach infinity (kx+b-(x^3+1)/(x^2+1)=0. Find the values of k and b
Combining the terms into one fraction, we have
[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]
If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.
To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have
[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]
Alternatively, we can compute the quotient and remainder of the rational expression.
[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]
Then in the limit, we have
[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]
Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].
The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed.
Estimate the percent of apartments residents who pay less than $650 per month.
A. 99%
B. 25%
C. 68%
D. 30%
Answer: 30%
Step-by-step explanation:
the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%
Answer:
30%
Step-by-step explanation:
For Connexus students its 30% :)
Suppose we want to choose 7 colors, without replacement, from 12 distinct colors?
792 different sets of 7 colors can be chosen.
In how many ways can be the 7 colors selected?Remember that if we have a set of N elements, the number of different sets of K elements that we can make out of these N elements is given by:
C(N, K) = N!/(N - K)!*K!
In this case, we have 12 distinct colors and we want to select 7, so we have:
N = 12
K = 7
Replacing that we get:
C(12, 7) = 12!/(12 - 7)!*7! = 12*11*10*9*8/(5*4*3*2*1) = 792
792 different sets of 7 colors can be chosen.
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Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)
Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:
[tex]v = \frac{12}{t}[/tex]
Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:
[tex]v + 6 = \frac{12}{3 - t}[/tex]
[tex]v = \frac{12}{3 - t} - 6[/tex]
Then:
[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]
[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]
[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]
18t - 6t² = 24t - 36
6t² + 6t - 36 = 0
t² + t - 6 = 0
(t + 3)(t - 2) = 0. -> t = 2 hours.
Hence her jogging rate in mph is given as follows:
[tex]v = \frac{12}{2} = 6[/tex]
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For Pharaoh Company, variable costs are 60% of sales,the fixed costs are $175,500. Managements net income goal is $67,500.
The required sales in dollars needed to achieve managements target is $607,5000.
What is the required level of sales?
Net income is total revenue less total cost. Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. e.g. rent. Variable cost is the cost that varies with output e.g. wages.
Net income = sales - total cost
Net income = sales - (fixed cost + variable cost)
$67,500 = sales - ($175,500 + 0.6sales)
$67,500 = sales - $175,500 - 0.6sales
$67,500 + $175,500 = sales - 0.6sales
243,000 = 0.4sales
sales = 243,000 / 0.4
sales = $607,500
Here is the complete question:
For Pharaoh Company, variable costs are 60% of sales, the fixed costs are $175,500. Managements net income goal is $67,500.Compute the required sales in dollars needed to achieve managements target net income of $67.500.
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The mean of a normally distributed data set is 110, and the standard deviation is 15.
a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 95.
b) Use the standard normal table to find the probability that a randomly-selected data value is greater than 125.
From the standard normal table, the respective probabilities are; 0.908 and 0.841
How to find the probability from z-score?
Formula for calculating the standard score or z score is:
z = (x - μ)/σ
where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
A) We are given;
x = 95
μ = 110
σ = 15
Thus;
z = (95 - 110)/15
z = 1.33
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.091759.
P(x > 95) = 0.908
B) We are given;
x = 125
μ = 110
σ = 15
Thus;
z = (125 - 110)/15
z = 1
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.158655.
P(x > 95) = 0.841
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The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 63% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 59%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level
Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of at most 59%, that is:
[tex]H_0: p \leq 0.59[/tex]
At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:
[tex]H_1: p > 0.59[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.59, n = 900, \overline{p} = 0.63[/tex]
Hence the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}[/tex]
z = 2.44.
What is the p-value and the conclusion?Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.
Since the p-value is less than 0.02, we reject the null hypothesis.
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On Monday, a local hamburger shop sold a combined total of 336 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday
Answer:
84
Step-by-step explanation:
Let the number of hamburgers be h and the number of cheeseburgers be c.
This means that:
h+c=336c=3hSubstituting c=3h into the first equation, it follows that 4h=336, and thus h=84.
In a village the cases of a particular infectious disease have been exponentially decreasing at a rate of 95% per year since the pople started receving the vaccine. If there were 200 cases in the village to start with, predict the number of cases after 2 years. First complete the equation:
Remaining amount=
The number of cases after two years is 221.
What is the number of cases after two years?As a result of the disease, the population of the village would decrease by 95% per year. The number of cases at the village is function of the rate of infection, the number of years and the beginning number of cases.
The exponential function that can be used to represent this situation is:
FV = P( 1 + r)^t
FV = Future value P =beginning number of casesR = rate of increase in the number of cases : 100% - 95% = 5%t = timeFV = 200 (1.05)^2 = 221
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Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z.
Answer:
one of several possible solutions :
18, 75, 105
Step-by-step explanation:
prime factors of 3150 :
3150 ÷ 2 = 1575
1575 ÷ 2 no
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 3 no
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 5 no
7 ÷ 7 = 1
3150 = 2¹ × 3² × 5² × 7¹
these are the product of the longest streaks of prime factors in x, y and z.
the GCF(y, z) = 15.
the prime factors of 15 are simply 3¹×5¹.
so, y and z share only the factors 3 and 5.
the GCF(x, y, z) = 3.
since x is an even number, the elimination of 5 in the GCF is not surprising.
let's try the following :
x = 2¹ × 3² = 2×9 = 18
y = 3¹ × 5² = 3×25 = 75
z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105
that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is
2¹ × 3² × 5² × 7¹.
fits.
the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.
fits.
the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.
fits.
18 < 75 < 105
fits.
18 is an even number greater than 10.
fits.
there are more than 1 solutions.
e.g.
z = 2¹ × 3¹ × 5¹ × 7¹ = 210
is also possible.
