Answer:
D. 77
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation is estimated to be $300
This means that [tex]\sigma = 300[/tex]
If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
This is n for which M = 80. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]
[tex]80\sqrt{n} = 2.327*300[/tex]
[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]
[tex]n = 76.15[/tex]
Rounding up:
77 cardholders should be sampled, and the correct answer is given by option d.
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many ounces of tomatoes paste are needed for every cup of water show your work.
Answer:
8 ounces of tomato paste for each cup of water.
Step-by-step explanation:
Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.
Hope this helps!
Work Shown:
48 oz of tomato paste = 6 cups of water
48/6 oz of tomato paste = 6/6 cups of water
8 oz of tomato paste = 1 cup of water
In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.
al calls every 3 days, lee every 4 days, and pat every 6 day. Once every ? days, all three will call on the same day
Answer:
12
Step-by-step explanation:
Find the LCM (Least Common Multiple) of the three numbers.
We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.
6 x 2 = 12
4 x 3 = 12
3 x 4 = 12
Hope this helps!
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.
A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.
Which expression represents the volume of the pyramid?
StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3
Answer:
Hello,
Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
Step-by-step explanation:
[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]
the third of the sum of the cube of x and double of the square of x ( cm³)
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
Area of the square base = x * x = x² cm²
Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)
Volume of pyramid = (x³ + 2x²) / 3
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
Find out more on volume at: https://brainly.com/question/12410983
WILL MAKE BRAINLIEST
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70
Answer:
The Hong Kong dollar equivalent of K70 is HK $ 94.71.
Step-by-step explanation:
Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:
1,353 x 70 = X
94.71 = X
Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
15
Simplify
a
25
O A. a3
O B. a10
O c. a-10
O D. a-3
Answer:
B is the correct answer of your question.
I HOPE I HELP YOU....
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
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Is 1 2/6 a rational number?
Answer:
Yes, it is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful.....In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
Determine the number positive real zeros of the polynomial below. (Type answer in as a whole number)f(x)=x^5+3x^2-4x+2
Answer:
The number of positive real zeros is 2 or 0
Step-by-step explanation:
Given
[tex]f(x)=x^5+3x^2-4x+2[/tex]
Required
Number of positive real zeros
Using Descartes rule of signs;
We write out the signs in front of each term;
Sign = + + - +
Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive
From positive to negative, we have: 1 (i.e. + - )
From negative to positive, we have: 1 (i.e. - +)
Add up the count
[tex]count = 1+1[/tex]
[tex]count = 2[/tex]
Hence, the number of positive real zeros is 2 or 0
compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest
Here, we want to find the interest rate and principal
The interest rate, r = 6% and the principal, P = Rs 65,000
Compound interest:
A = P(1 + r/n)^t
Simple interest :
I = P * r * t
Simple interest for 2 years = Rs 7800
Simple interest for 1 year = Rs 7800 / 2
= Rs 3900
Compound interest for 2 years = Rs 8034
Compound interest for the second year = Rs 8034 - Rs 3900
= Rs 4134
Interest on Rs 3900 = Rs 4134 - Rs 3900
= Rs 234
Therefore,
Interest rate, r = 234/3900 × 100
= 0.06 × 100
r = 6%
Recall,
Simple interest :
I = P * r * t
Then,
P = I / r * t
= 3900 / 6% * 1
= 3900 / 0.06
= 65,000
P = Rs 65,000
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For a standard normal distribution, find:
P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.
Answer:
P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960
Help please:))
2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.
Remember that for a cylinder of radius R and height H the volume is:
V = pi*R^2*H
And the surface will be:
S = 2*pi*R*H + pi*R^2
where pi = 3.14
Here we know that the volume is 1000cm^3, then:
1000cm^3 = pi*R^2*H
We can rewrite this as:
(1000cm^3)/pi = R^2*H
Now we can isolate H to get:
H = (1000cm^3)/(pi*R^2)
Replacing that in the surface equation, we get:
S = 2*pi*R*H + pi*R^2
S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2
S = 2*(1000cm^3)/R + pi*R^2
So we want to minimize this.
Then we need to find the zeros of S'
S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0
So we want to find R such that:
2*pi*R = (2000cm^3)/R^2
2*pi*R^3 = 2000cm^3
R^3 = (2000cm^3/2*3.14)
R = ∛(2000cm^3/2*3.14) = 6.83 cm
The radius that minimizes the surface is R = 6.83 cm
With the equation:
H = (1000cm^3)/(pi*R^2)
We can find the height:
H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm
(so the height is equal to the radius)
b) The surface equation is:
S = 2*pi*R*H + pi*R^2
replacing the values of H and R we get:
S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2
c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.
Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
Not sure how to do this
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
What is the value of the expression 10(6 + 5)² when b = 3?
10(3+5)^2
10(8)^2
10(64)
=640
Hii guys if you have time plz help me
Answer:
[tex]5 {x}^{2} + 21 + 5x[/tex]
Step-by-step explanation:
TOTAL AMOUNT earned = Tim money + Melina money
[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]
[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]
[tex] = 5 {x}^{2} + 21 + 5x[/tex]
What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12
Answer:
8
Step-by-step explanation:
To determine the common difference, take the second term and subtract the first term
11-3 = 8
Check with the other terms in the sequence
19-11= 8
27-19 = 8
35-27=8
The common difference is 8
Answer:
C. 8
Step-by-step explanation:
There is a common difference between them and that’s 8.
3 + 8 = 11
11 + 8 = 19
19 + 8 = 27
27 + 8 = 35
Answer this please~!!!!
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
HELP PLZ<3
An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
Answer:
82991 employees
Step-by-step explanation:
One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that
28300 = 34.1%
If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get
829.912 = 1%
Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get
100% = 82991
Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.
Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.
The condition is shown in the diagram.
Then the height of the wall will be
[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]
More about the right-angle triangle link is given below.
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If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
Use the information below to complete the problem: p(x) = (1)/(x + 1)
and q(x) = (1)/(x - 1)
Perform the operation and show that it results in another rational expression.
p(x) - q(x)
Given:
The functions are:
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
To find:
The rational expression for [tex]p(x)-q(x)[/tex].
Solution:
We have,
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
Now,
[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]
[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]
[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]
Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].
wrote the terms below.
–8, –4, 0, 4, 8, 12
What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
Answer:
an arithmetic sequence
Step-by-step explanation:
an arithmetic series is wrong also heres an example i found of an arithmetic sequence
The terms in the given sequence represents an arithmetic sequence.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence of numbers is,
-8, -4, 0, 4, 8, 12, ......
We have to find which sequence does it represent.
This is not a series since they are not represented as the sum.
If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.
If it is arithmetic sequence, then the difference of consecutive numbers will be same.
Here, ratio is not same.
Difference are same.
-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........
Common difference is 4.
Hence it is an arithmetic sequence.
Learn more about arithmetic Sequence here :
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a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by
Complete Question:
A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer:
a. $450
b. 1500 cans
Step-by-step explanation:
Given the following quadratic function;
P(x) = -0.001x² + 3x - 1800 ......equation 1
a. To find his maximum profit per day;
Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]
Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2
Comparing eqn 1 and eqn 2, we have;
a = -0.001, b = 3 and c = -1800
Now, we determine the maximum profit;
[tex] x = \frac {-b}{2a} [/tex]
Substituting the values, we have;
[tex] x = \frac {-3}{2*(-0.001)} [/tex]
Cancelling out the negative signs, we have;
[tex] x = \frac {3}{2*0.001} [/tex]
[tex] x = \frac {3}{0.002} [/tex]
x at maximum = 1500
Substituting the value of "x" into equation 1;
P(1500) = -0.001 * 1500² + 3(1500) - 1800
P(1500) = -0.001 * 2250000 + 4500 - 1800
P(1500) = -2250 + 2700
P(1500) = $450
b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.
Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?
Answer: 14 seed packs
Step-by-step explanation:
You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.
The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard deviation of 6 seconds. What travel time separates the top 2.5% of the travel times from the rest
Answer:
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 80 seconds and a standard deviation of 6 seconds.
This means that [tex]\mu = 80, \sigma = 6[/tex]
What travel time separates the top 2.5% of the travel times from the rest?
This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 80}{6}[/tex]
[tex]X - 80 = 6*1.96[/tex]
[tex]X = 91.76[/tex]
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
