The critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
How to find the critical value?We want to find the two tail critical values.
This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.
Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.
However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.
From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;
z = 1.41
Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
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Finding a percentage of a total amount: Real-world situations
A file that is 258 megabytes is being downloaded. If the download is 13.3% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth.
Answer: 34.3 megabytes
Step-by-step explanation:
To find how many megabytes have been downloaded you must multiply 13.3% by 258. 13.3% can be written as the decimal 0.133
Now let's multiply
[tex]258[/tex]×[tex]0.133[/tex]=34.314
Rounded to the nearest tenth that is 34.3
A recipe for a single batch of cookies calls for 3 eggs.
Step 1. Write an equation that represents the total number of eggs we need (n) for some batches (b) of this recipe.
Step 2. How many eggs do we need to make 6 batches of this recipe?
The total number of eggs needed for b batches is n = 3b
The total number of eggs needed for 6 batches is 18.
How many eggs are needed?
Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.
In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.
Total eggs needed = eggs needed for one batch x total number of batches
n = 3 x b
n = 3b
6 x 3 = 18
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[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation
Assuming you mean
[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]
where
[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]
we have by the binomial theorem
[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]
so that the given sum has a value of [tex]\boxed{2^n}[/tex].
The formula for the perimeter of a rectangle is 2L + 2W = P (L = length, W = Width and P = Perimeter.) The perimeter of a rectangular garden is 400 feet. If the length of one side of the garden is 120 feet, what is the width of one side of the garden?
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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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pops on the upward faces of the 2 dice is the following. 1
Answer: 0
Step-by-step explanation:
[tex]h(x) = x -1 + \frac{1+ ln {}^{2} (x) }{x}[/tex]
[tex]\displaystyle \lim_{x\to0} h(x)= \: ? \\ \displaystyle \lim_{x\to \infty } h(x)= \: ?[/tex]
Apply L'Hôpital's Rule if possible
Answer:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
Step-by-step explanation:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]
= +∞ + 0
= +∞
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]
= -1 + +∞
= +∞
9e-6(-2e+7)= please help me solve this problem
[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]
Step-by-step explanation:
[tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]
we first must use the distributive property. You can think about solving this like this:
[tex]=9e-(6)(-2e+7)[/tex]
Notice how we are not distributing -6, but only 6. Now we can solve normally:
[tex]=9e-(-12e+42)[/tex]
Now we distribute the '-' sign to the terms in parenthesis.
[tex]=9e+12e-42[/tex]
[tex]\longrightarrow \large\boxed{21e-42}[/tex]
The decimal form is 15.08 rounded.
Please hurry quick I need an answer
Answer:
slope is 4
Step-by-step explanation:
Slope is rise/run
for every 4 units it rises it runs 1 unit
4/1=4
How many three-digit positive integers have three different digits and at least one prime digit?
Answer:
252
Step-by-step explanation:
using a brute force method in c++
#include <stdio.h>
int main(){
int a, b, c, n = 0;
for(a = 1; a <= 9; a++)
for(b = 0; b <= 9; b++)
for(c = 0; c <= 9; c++)
if((a==3 || b==3 || c==3)) n++;
printf("%d\n", n);
}
A _____ is a solid consisting of a suite a point not in the same plane as the square and all points between them
Answer:
Square Pyramid
Step-by-step explanation:
Thats what a Square Pyramid is
15. Michael, the art elective programme student,
is working on another assignment. He designs a
rectangular pattern measuring 45 mm by 42 mm.
He is required to use identical rectangular patterns to
form a square. The maximum area of the square
allowed is 1.6 m².
(i) How many patterns does he need to form the
smallest square?
(ii) What are the dimensions of the largest square
that he can form?
Step-by-step explanation:
1 meter = 1000 mm
the area of 1.6 m² means the side length of the square is
sqrt(1.6) = 1.264911064... m = 1,264.911064... mm
to create a square out of the rectangular pattern he needs to put e.g. 42 patterns along the 45 mm side and stack 45 patterns on top of the 42 mm side.
the minimum number of needed patterns we get via the last common multiple (LCM) of 42 and 45.
for this we use the prime factorization :
45 ÷ 2 no
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
45 = 3² × 5¹
42 ÷ 2 = 21
21 ÷ 2 no
21 ÷ 3 = 7
7 ÷ 3 no
7 ÷ 5 no
7 ÷ 7 = 1
42 = 2¹ × 3¹ × 7¹
the LCM is the product of the longest streaks of each used prime factor.
LCM(42, 45) = 2¹ × 3² × 5¹ × 7¹ = 2×9×5×7 = 630
(i) he needs 210 patterns to form the smallest square.
this will be
14×45 mm on one side = 630 mm
15×42 mm on the other side = 630 mm
14×15 = 210 patterns.
(ii)
the limit per side length is as established
1,264.911064... mm
starting with the minimum of 630 mm how often can we add 42 mm in one direction and 45 mm in the other, and keep a 15 : 14 ratio between these numbers ?
and we need integer numbers, as we cannot use parts of the patterns (only full patterns).
45 × x <= 1264
x <= 1264/45 = 28.08888888... = integer 28
42 × y <= 1264
y <= 1264/42 = 30.0952381... = integer 30
30/28 = 15/14
so, the ratio is maintained for these numbers.
that means as maximum we can put
30×28 = 840 patterns as square inside the max. allowed area.
the dimensions of this max. square are therefore
30×42 = 1260 mm
28×45 = 1260 mm
the area of this square is then
1260mm × 1260 mm = 1,587,600 mm² = 1.5876 m²
3. Complete the table (showing work) and draw a graph of the logarithmic function f(x) = log 1/5 x
Answer:
Step-by-step explanation:
First dispensed is 1/3 of a quart, later 1/4and then you dispensed 3 1/2 quarts. What’s the total volume that is dispensed
Answer:4 1/12.
Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4. Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].
We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].
[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:
[tex]x^{2} +y^{2} -2x+1-9=0[/tex]
[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]
[tex](x-1)^{2}+y^{2}[/tex]-9=0
[tex](x-1)^{2} +y^{2} =9[/tex]
[tex](x-1)^{2}+y^{2} =3^{2}[/tex]
Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.
From the comparison of both the equations we get that radius is 3 units.
From the equation point will be (1,0). It is on the x axis.
Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
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Answer: 1,2,5 on edge
Step-by-step explanation:
see above ans for work
sin theta =-(1)/(\sqrt(17))and (3\pi )/(2)<=\theta <=2\pi then tan\theta =
Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:
tan(theta) = -1/4
Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
For this problem, the sine is given as follows:
[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]
Then the cosine, which we need to find the tangent, is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{16}{17}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]
Since the angle is in the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]
What is the tangent of an angle?It is the sine of the angle divided by the cosine of the angle, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]
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3
Select the correct answer.
What is the inverse of the function f(x)=19/x2
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
What is the meaning of inverse function?An inverse function in mathematics exists function which "reverses" the another function.
Let f(x) = y, then the inverse function, [tex]$x=f^{-1}(y)$[/tex]
[tex]$&f(x)=\frac{19}{x^{2}} \\[/tex]
[tex]$&y=\frac{19}{x^{2}} \\[/tex]
[tex]$&x^{2}=\frac{19}{y} \\[/tex]
simplifying the equation, we get
[tex]$&x=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&f^{-1}(y)=\sqrt{\frac{19}{y}},[/tex] then [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
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A garrison has provision for 10 days. At the end of 2 days 1/2 of the men left the garrison. how long the food will now last?
Please answer with explanation?
After half of the men go away, the provisions will last for another 16 days.
how long the food will now last?
First, we know that the garrison has provisions for 10 days.
2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.
So we just need to solve the product:
2*8 days = 16 days.
After half of the men go away, the provisions will last for another 16 days.
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Multiply each of the following(2a-3b)and(a^2+2b^2)
Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]
Step-by-step explanation:
Given expression
(2a - 3b) (a² + 2b²)
Apply the FOIL method (First Outer Inner Last)
Please refer to the attachment below for a graphical understanding
= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²
Simplify by multiplication
=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)
[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Your answer is 2a³ + 4ab² - 3a²b - 6b³.
Step-by-step explanation:
(2a - 3b) (a² + 2b²)
=2a (a² + 2b²) -3b (a² + 2b²)
=2a.a² + 2a.2b² - 3b.a² - 3b.2b²
=2a³ + 4ab² - 3a²b - 6b³ ans.
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The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the following:Angle of measure 78 degree enclosed by the diagonals of the rectangle
Perimeter = 36 cm
To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.
A side of the rectangle = x cm
The other side = (36 - 2x)/2 = (18 - x) cm
Angle of the diagonal base = (180 - 78)/2 = 51°
Apply the tangent ratio to find x:
Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,
∅ = 51°
Opposite side = x cm
Adjacent side = (18 - x) cm
Tan 51° = x/(18 - x)
1.235 = x/(18 - x)
1.235(18 - x) = x
22.23 - 1.235x = x
22.23 = x + 1.235x
22.23 = 2.235x
22.23/2.235 = 2.235x/2.235
x = 9.946 cm (one side length)
The other side length = 18 - x = 18 - 9.946 = 8.054 cm
Area of the rectangle = (9.946)(8.054)
Area of the rectangle = 80.1 cm²
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solve for x in the diagram
sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3
Answer: [tex]\Large\boxed{x=12}[/tex]
Step-by-step explanation:
Given information
∠1 = x + 42°
∠2 = 3x°
Total Angle = 90° (Right Angle)
Derived formula from the given information
∠1 + ∠2 = Total Angle
Substitute values into the given formula
(x + 42) + (3x) = (90)
Combine like terms
x + 3x + 42 = 90
4x + 42 = 90
Subtract 42 on both sides
4x + 42 - 42 = 90 - 42
4x = 48
Divide 4 on both sides
4x / 4 = 48 / 4
[tex]\Large\boxed{x=12}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the name for a mathematical phrase? O A. An inequality OB. An operation OC. An expression OD. An equation
polygon h is a scaled factor of polygon g using a scale factor of 1/4
The fraction of the area of polygon H of polygon G's area would be: 1/16.
What are Similar Polygons?When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.
What is a Scale Factor?The scale factor = new dimension/original dimension
Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:
Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation
Area of polygon H/Area of polygon G = 1²/4² = 1/16
This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².
Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.
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How is a marketing -oriented firm different from a production-oriented firm or a sales-oriented firm?
Marketing-oriented firms focus more on what the market needs above every other aspects.
What is a Marketing-oriented Firm?Marketing-oriented firms can be described as firms that major in identifying the needs and wants of customers and then creating specific products that are designed to meet the wants of such customers. One of the important elements of marketing-oriented firms is to ensure there is a demand for whatever products or services they offer.
Some examples of marketing-oriented firms are:
AppleCoca-ColaAmazonWhat is a Product-oriented Firm or a Sales-oriented Firm?A product-oriented firm focus more resources on and focus on researching and developing quality products rather than focusing more on the market to discover the wants of customers.
Sales-oriented firm tend to focus more on developing its sales force that will promote their products and services.
How Marketing-Oriented Firms are Different from the Product-oriented or Sales-oriented Firms?Marketing-oriented firms stand out and are different from the other two types of firms because they focus more on what the market needs above every other aspects.
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Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B? (5 points)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.
Given Information:
For circle A,
Center, C1(x, y) = (6, 7)
Radius, r1 = 4
For circle B,
Center, C2(x, y) = (2, 4)
Radius, r2 = 16
Showing the Two Circles Similar
Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:
First, translate circle A using the rule (x + 4, y + 3).Then, rotate circle A by 45° about the center.In the third step, dilate circle A by a scale factor of 4 (r2/r1).Finally, Reflect circle A about the origin to make it similar to circle BHence, we can now see that circle A is similar to circle B.
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Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5
Answer: -6
Step-by-step explanation:
[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]
So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.
Substituting into point-slope form, the equation is
[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]
Converting to the required form,
[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]
So, B-A is equal to -6.
(1,-2) and (2,-4) exponential formula f(x)=ab^x
We conclude that the exponential function is:
f(x) = -1*(2)ˣ
How to find the exponential function?Here we know that we have an exponential function of the form:
f(x) = a*b^x
And we know two points on the function, that are:
f(1) = -2 = a*b^1 = a*b
f(2) = -4 = a*b^2
Then we have a system of equations to solve, which is:
-2 = a*b
-4 = a*b^2
From the first equation we can solve:
-2/a = b
Replacing that in the other equation we can get:
-4 = a*(-2/a)^2 = 4/a
a = 4/-4 = -1
Now that we know the value of a, we can get the value of b:
-2/a = b
-2/-1 = 2 = b
In this way, we conclude that the exponential function is:
[tex]f(x) = -1*(2)^x[/tex]
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A man can take a same time to row 13km downstream and 7km upstream.His speed in still water is 5km/hr.The speed of stream is
Answer:
0.6 km/hr
Step-by-step explanation:
Speed downstream: 13/5= 2.6 km/hr
Speed upstream: 7/5= 1.4 km/hr
Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr
How many three-digit positive integers have three different digits and at least one prime digit?
The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.
The only two components in prime numbers are 1 and the number itself.
Any whole number greater than one is a prime number.
It has exactly two factors—1 and the actual number.
There is just one 2-digit even prime number.
Every pair of prime numbers is always a co-prime.
The product of prime numbers can be used to represent any number.
Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960
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thank you for helping
I need help solving this problem!
Answer: A
Step-by-step explanation:
The domain is the range of possible x that doesn't make y impossible to find, in this case, all real numbers work
The range is the range of possible y that doesn't make x impossible to find in the inverse function, in this case, all real numbers work
The answer is A.
As any number can be replaced in place of x for the function y, the domain of the function is All Real Numbers. Since any number can be inputted, the result will also vary accordingly. Hence, the range of the function is All Real Numbers.
This is true for the listed function :
[tex]\boxed {y = \sqrt[3]{x-2} - 5}[/tex]