The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
How to determine the probability?The given parameters are:
Sample size, n = 100Population proportion, p = 82%Start by calculating the mean:
[tex]\mu = np[/tex]
[tex]\mu = 100 * 82\%[/tex]
[tex]\mu = 82[/tex]
Calculate the standard deviation:
[tex]\sigma = \sqrt{\mu(1 - p)[/tex]
[tex]\sigma = \sqrt{82 * (1 - 82\%)[/tex]
[tex]\sigma = 3.84[/tex]
Within ± 0.02 of the population proportion are:
[tex]x_{min} = 82 * (1 - 0.02) = 80.38[/tex]
[tex]x_{max} = 82 * (1 + 0.02) = 83.64[/tex]
Calculate the z-scores at these points using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z_1 = \frac{80.36 - 82}{3.84} = -0.43[/tex]
[tex]z_2 = \frac{83.64 - 82}{3.84} = 0.43[/tex]
The probability is then represented as:
P(x ± 0.02) = P(-0.43 < z < 0.43)
Using the z table of probabilities, we have:
P(x ± 0.02) = 0.3328
Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
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Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?
Complete the remainder of the
table for the given function rule:
y = ²x + 4
X-6 -3 03 3 6
y 0 [?] [] [] []
Answer: 2, 4, 6, 8
Step-by-step explanation:
Just plug x into the equation for each one.
x = -3
[tex]y=\frac{2(-3)}{3} +4\\y=\frac{-6}{3} +4\\y=2[/tex]
With this one, you can see it is a linear equation and for every increase of 3 on x, y in increased by 2.
x -6 -3 0 3 6
y 0 2 4 6 8
4. During a camping trip, a group went one-third of the total distance by boat, 10km by foot and One-sixth of it by riding horses. Find the total distance of the trip. Plss answer thiissss
Answer:
20 km
Step-by-step explanation:
So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2
Meaning the 10 km by foot left is the other half
Select the correct answer. Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0
Answer: 0
Step-by-step explanation:
[tex](h \circ k)(1)=h(k(1))=h(4)=\boxed{0}[/tex]
Lief starts saving for his future and deposits $425 each month at 5.7% annual interest, compounded monthly, for 25 years. At the end of 25 years, he has an account balance of $281,292.21. How much of this did Lief contribute and how much of this is interest?
Using proportions, it is found that the amounts are given as follows:
Amount deposited: $127,500.Amount of interest: $153,792.21.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The amount deposited is of $425 each month for 25 years, that is, $425 in 25 x 12 times, that is:
D = 425 x 25 x 12 = $127,500.
The amount of interest is the total amount subtracted by the amount deposited, hence:
I = 281,292.21 - 127,500 = $153,792.21.
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The temperature of a chemical reaction ranges between -10 degrees Celcius and 50 degrees Celcius. The temperature is at its lowest point when t=0, and the reaction completes 1 cycle during a 6 hour period. What is a cosine function that models this reaction?
Answer:
The cosine function is f(t) = -30sin(π÷3)t + 20
Step-by-step explanation:
Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.
To find : What is a cosine function that models this reaction?
General form of cosine function is f(x) = A cos(Bx)+C
Where A is the amplitude
B=2π÷Period
C is the midline
Now, We have given
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.
A is the average of temperature,
i.e,
A=(-10-50)÷2 = -30
Period of 1 cycle is 6 hour
So,
B = 2π÷6 = π÷3
The temperature is at its lowest point when t = 0 and we know lowest point is -10
So,
f(t) = A cos t + C
-10 = -30 cos 0 + C
Therefore, C = 20
Substituting the values, we get
The cosine function is f(t) = -30sin(π÷3)t + 20
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Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{2}(6)(4)(2)=\boxed{24}[/tex]
? Question
Select the graph of the transformation.
The graph f(x)=√√ is transformed to form
shows g(x).
Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.
please help me.
Which quantity is multiplied by pi () in the formula for the area of a circle?
A. d
OB. 2
O c. d
D. r
Can you do this because it is confusing to me
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 1330.4644 cm³.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
Given the height of the cylinder is 14 cm, while the diameter of the cylinder is 11 cm. Therefore, the volume of the cylinder can be written as,
The volume of the cylinder = (π/4)×(D²) × H
= (π/4)×(11)² × 14
= 1330.5 cm³
Hence, the volume of the cylinder is 1330.5cm³.
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2. Ahmed has ¢15.25 and spent $7.50 at the
Total Shop. How much money does he have
left?
Answer:
D)¢ 8.75
Step-by-step explanation:
that is my answer please
The circle below is centered at the point (-1, 2) and has a radius of length 3.
What is its equation?
O A. (*+ 1)2 + (y- 2)2 = 9
O B. (x- 2)2 + (y + 1)? =
32
O c. (x- 1)2 + (y + 2)2 = 9
l
O D. (x+ 2)2 + (y- 1)2 =
32
Answer:
it should be option A
and in option there should be "x" instead of "*"
Equation of circle is,
⇒ (x + 1)² + (y - 2)² = 9
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle below is centered at the point (-1, 2) and has a radius of length 3.
Now, We get;
The equation of circle is,
⇒ (x - (- 1))² + (y- 2)² = 3²
⇒ (x + 1)² + (y - 2)² = 9
Thus, Equation of circle is,
⇒ (x + 1)² + (y - 2)² = 9
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The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?
Step-by-step explanation:
you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...
1 hamburger = $2.50
5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50
that leaves for the 11 pizzas (slices)
40 - 12.5 = $27.50
so, 1 pizza (slice) is
27.5 / 11 = $2.50
Answer:
One hamburger costs $2.50
One pizza also costs $2.50
Step-by-step explanation:
Let's say Nigel is the one purchasing lots of food for no reason.
Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)
We can write this algebraically:
11p + 5b = 40
We know that the price of 1 Hamburger is $2.50.
Now we can plug that into out equation and find the price of one pizza:
11p + 5(2.50) = 40
11p + 12.5 = 40
11p = 27.5
p = 2.5
Now, we have the price of one pizza, $2.50
Y=-1/3x+2
A.
B.
C.
D.
Answer:
C
Step-by-step explanation:
The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)
The y intercept is 2.
y=x^2 -2x -3 im not sure how to solve this
Answer:
It is solved on a graph
Step-by-step explanation:
A quadratic graphical solution.
You invested $7,000 into a money market account for 10 years at an annual interest rate of 3%. How much is the accrued interest?
The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.
What is invested amount?An investment is a payment made to acquire the securities of other firms with the intention of making a profit.
We are assuming the interest will be compounded annually
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
P = $7000
r = 3% = 0.03
t = 10 years
n = 1
[tex]\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}[/tex]
After calculating:
A = $9407.41
I = A - P = 9407.41 - 7000 = $2,407.41
Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.
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3.14(a2 + ab) when a = 4 and b = 3
Step-by-step explanation:
how does the picture fit into this question ?
I guess you mean
(a² + ab)
when a = 4 and b = 3. then we simply replace the variable names by the actual values and calculate :
4² + 4×3 = 16 + 12 = 28
.
now to the picture :
i am not sure what the requested result of procedure is.
so, I am just going to simplify the expression :
(log(25) - log(4)) / (log(55) - 1/2 × log(2)
remember the rules of the logarithm :
log(a) - log(b) = log(a/b)
k × log(a) = log(a^k)
a^(1/2) = sqrt(a) (the square root of a)
I assume we are using the logarithm to the base of 10.
so, we have here
log(25/4) / log(55/sqrt(2)) =
= 0.795880017... / 1.589847692... = 0.500601423...
According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ
Answer:
OD.(x-3)(x-2)
Step-by-step explanation:
we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.
so its OD
as -3×-2=6
and -3+-2=-5
A building has a height of 40 feet and a length of 20 feet. On a scale drawing of the building, the height is 20 centimeters. What is the length of the building on the scale drawing in centimeters?
Answer:
10 centimeters
Step-by-step explanation:
For the height:
40 ft / 20 cm = 2 ft / cm
With this ratio, we find the length as follows:
2 ft / cm = 20 ft / x cm
[tex]2 = \frac{20}{x} [/tex]
[tex]2x = 20[/tex]
[tex]x = 10[/tex]
Answer:
10 cm
Step-by-step explanation:
Look at the answer
Find the equation of a line that is perpendicular to Y= 4X +5 that passes through (2,-5)
Answer:
4y +x =18
Step-by-step explanation:
y - (-5) -1
----------- = ------
x - 2 4
4y +20 = -x+2
4y +x =18
What is 60 percent of 92?
•
1.53
•
5.52
•
15.3
O 55.2
49:03 mins pls help me with this
60 percent of 92 is 55.2
How to determine the percentage?The statement is given as:
60 percent of 92
This means:
60% of 92
Express of as *
60% * 92
Evaluate the product
55.2
Hence, 60 percent of 92 is 55.2
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Please hurry!!!! What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0
A. all real numbers
the doman are the x values and in this equation they are infinite making the domain all real numbers
Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 2 x + 4 y ≤ 36 7 x + 5 y ≤ 63 x ≥ 0 y ≥ 0 { 2x+4y ≤ 36 7x+5y ≤ 63 x ≥ 0 y ≥ 0
Feasible region for the given inequalities is shaded via black color in graph.
What is Inequalities?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Here, given Inequalities are;
2 x + 4 y ≤ 36
7 x + 5 y ≤ 63
x ≥ 0 y ≥ 0
The graph of given inequalities are given below and the feasible region is shaded with the black color.
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Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]
[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]
[ log (x) + log (y) = log (xy) ]
[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]
[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]
The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[15 PTS] PLS HELP!!!
What is the end behavior of the function?
The correct answer is the fourth option.
How to do this please?️
Step-by-step explanation:
Using dimensional analysis, let convert km to cm.
[tex] \frac{4cm}{1km} \times \frac{km}{100000 \: cm} [/tex]
Cancel out the km
[tex] \frac{4cm}{100000 \: cm} [/tex]
[tex] \frac{1}{25000 } [/tex]
So n= 25000
iii.
Dimensional Analysis
[tex] \frac{3 \: cm}{1 } \times \frac{km}{100000 \: cm} [/tex]
[tex] \frac{3 \: km}{100000} [/tex]
Or
[tex]0.00003 \: km[/tex]
John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4
Option D is the correct answer.
All real numbers greater than or equal to 0 and less than 4.
What is Domain?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.
Here, The function of the car value is given as:
V(x) = 20000 X (0.84)ˣ
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ
10000 = 20000 X (0.84)ˣ
Divide both sides by 20000
0.84ˣ = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4.
Thus, all real numbers greater than or equal to 0 and less than 4.
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Somebody help me solve;
(1)A fair die is being rolled.
a) Find the probability that at least 5 rolls are needed to obtain the first
one.
b) Find the probability that it will take fewer than seven rolls to obtain the
second one if the first one occurs on the third roll.
If BC is 1
CD is 2
DA is 3
AB is 4,
what is EF?
The length of the side EF will be 1 unit, approximately.
The complete figure is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is given below.
The length of EF will be
EF = CF – CE
Then the value of CF will be
CF = BC × cos 30
CF = 2 × 0.866
CF = 1.732
Then the value of CE will be
CE = BC × cos 42
CE = 1 × 0.743
CE = 0.743
Then we have
EF = 1.732 – 0.743
EF = 0.989 ≈ 1
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find the distance between the pair of points (7,6) and (4,10)
Answer:
5 units
Step-by-step explanation:
to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10
then you would square them and then add them
lastly you would take the square root of that and youd have your answer
so
7 - 4 = 3
6 - 10 = -4 (just use 4)
3^2 + 4^2 = 9 + 16 = 25
then you take the square root of this
sqrt(25) = 5
that is your answer
To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.
Set Up the Distance FormulaThe Distance Formula is defined as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We must title our points by the standard coordinate naming system:
[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]
Therefore, our points can be labeled:
[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]Substitute Known Values for VariablesNow, substitute the known values as the variables in the Distance Formula:
[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]
You must know the BPEMDAS acronym, which stands for:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Simplify the expression using BPEMDAS:
[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]
Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:
[tex]-3\times-3 = 9[/tex]
[tex]4\times4=16[/tex]
Simplify further by removing the parentheses:
[tex]d=\sqrt{9+16}[/tex]
Compute the additive operation:
[tex]d=\sqrt{25}[/tex]
Simplify the RadicandThe number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.
In this situation, the radicand is 25.
To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.
In this case, we can determine that 5² will result in a final answer of 25.
[tex]5^{2} = 25[/tex]
The final answer is 5 units.
