The equation that will represent this situation will be:
[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]Thus:
[tex]\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.
Answer: z-score is 0.063.
Given the following confidence interval for a population mean compute the margin of error E
Given that the Confidence Interval for a population mean:
[tex]11.81<\mu<13.21[/tex]In this case, you can set up these two equations:
[tex]\bar{x}+E=13.21\text{ \lparen Equation 1\rparen}[/tex][tex]\bar{x}-E=11.81\text{ \lparen Equation 2\rparen}[/tex]Because by definition:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex]Where "ME" is the margin of error and this is the mean:
[tex]\bar{x}[/tex]In this case, in order to find the "ME", you need to follow these steps:
1. Add Equation 1 and Equation 2:
[tex]\begin{gathered} \bar{x}+E=13.21 \\ \bar{x}-E=11.81 \\ -------- \\ 2\bar{x}=25.02 \end{gathered}[/tex]2. Solve for the mean:
[tex]\begin{gathered} \bar{x}=\frac{25.02}{2} \\ \\ \bar{x}=12.51 \end{gathered}[/tex]3. Substitute the mean into Equation 1 and solve for "ME":
[tex]12.51+E=13.21[/tex][tex]\begin{gathered} E=13.21-12.51 \\ E=0.7 \end{gathered}[/tex]Hence, the answer is:
[tex]E=0.7[/tex]three more than the difference of five and a number
Answer:
5x+3
Step-by-step explanation:
Three more than means we add 3
The product of 5 and a number means some number multiplied by 5 call it 5x
so three more than 5x is 5x+3.
An elliptical-shaped path surrounds a garden, modeled by quantity x minus 20 end quantity squared over 169 plus quantity y minus 18 end quantity squared over 289 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?
In general, the equation of an ellipse centered at (h,k) and axis equal to a and b, and parallel to the y-axis is
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1,a>b[/tex]And the maximum distance between two points on the ellipse is equal to the length of the major axis; in our case,
[tex]\begin{gathered} a^2=289,b^2=169 \\ \Rightarrow a=17,b=13 \end{gathered}[/tex]Therefore, the answer is 17 feet, the major axis.
find the intercepts and graph the equation by plotting points. 13^2 + 4y = 52
ANSWER
[tex]y-intercept:(0,-\frac{117}{4})[/tex]Graph:
EXPLANATION
Given:
[tex]13^2+4y=52[/tex]Desired Results:
Intercepts and graph the equation
Solve for y
[tex][/tex]Which of the following is a factor of the polynomial Step By Step Explanation Please
Use the quadratic formula.
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 3, b = -31, and c = -60.
[tex]x=\frac{-(-31)\pm\sqrt[]{(-31)^2-4(3)(-60)}}{2(3)}[/tex]Solve to find both solutions.
[tex]x=\frac{31\pm\sqrt[]{961+720}}{6}=\frac{31\pm\sqrt[]{1681}}{6}=\frac{31\pm41}{6}[/tex]Rewrite the expression as two.
[tex]\begin{gathered} x_1=\frac{31+41}{6}=\frac{72}{6}=12 \\ x_2=\frac{31-41}{6}=\frac{-10}{6}=-\frac{5}{3} \end{gathered}[/tex]Once we have the solutions, we express them as factors. To do that, we have to move the constant to the right side of each equation.
[tex]\begin{gathered} x=12\to(x-12) \\ x=-\frac{5}{3}\to(3x+5)_{} \end{gathered}[/tex]As can observe, the factor of the polynomial is (x-12).
Therefore, the answer is d.laws exponents multiplication band power to a power simplifymake it small steps please the smallest you canbare minimum of steps
Answer:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)=-12r^6s^{-4}[/tex]Explanation:
Given the expression:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)[/tex]This can be rearranged using law of multiplication (That multiplication is cummutative) to become:
[tex](4)(-3)(r^4rr)(s^{-2}s^{-3}s)[/tex]This becomes, using the law of exponents:
[tex]-12r^{4+1+1}s^{-2-3+1}[/tex]and finally, we have:
[tex]-12r^6s^{-4}[/tex]Kaitlin races her bicycle for 98 m. A wheel of her bicycle turns 49 times as the bicycle travels this distance. What is the diameter of the wheel? Use the value 3.14 for n. Round your answer to the nearest tenth
Answer:
0.6m
Explanation:
Given the following
Total distance covered = 98m
pi = 3.14
Circumference of the wheel is the distance travelled in one rotation. Hence;
distance travelled in one rotation = \pi d
d is the diamter of the wheel
distance travelled in 49 rotation = 49*\pi d
Since distance travelled in 49 rotation = 98m, then;
98 = 49*\pi d
Divide both sides by 49
98/49 = \pi d
2 = 3.14d
d = 2/3.14
d = 0.6m
Hence the diameter of the wheel is 0.6m
what is the y intercept of y = 250 + 15x
The y-intercept of y = 250 + 15x is (0,250)
What is y-intercept?A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
Here to determine the y-intercept put x=0,
Given, y = 250 + 15x
Replacing x by 0 in the above equation we get,
y = 250 + 15×0
y=250 +0
y=250
Therefore, the y-intercept of y = 250 + 15x is (0,250)
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Simplify the following equations in ax^2+bx+c=0 or ay^2+c=0 2x+y=6 4x^2+5y+y+1=0
Given the equation;
[tex]4x^2+5y^2+y+1=0[/tex]We shall begin by Subtracting 5y^2 + y from both sides;
[tex]\begin{gathered} 4x^2+5y^2+y+1-5y^2-y=0-5y^2-y \\ 4x^2+1=-5y^2-y \\ \text{Factor out -1 from the right hand side;} \\ 4x^2+1=-1(5y^2+y) \end{gathered}[/tex]Next step we subtract 1 from both sides;
[tex]\begin{gathered} 4x^2+1-1=-1(5y^2+y)-1 \\ 4x^2=-(5y^2+y)-1 \\ \end{gathered}[/tex]Next step we take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{4x^2}=\pm\sqrt[]{-(5y^2+y)-1} \\ 2x=\pm\sqrt[]{-(5y^2+y)-1} \end{gathered}[/tex]We can now open the parenthesis on the right hand side;
[tex]\begin{gathered} 2x=\pm\sqrt[]{-5y^2-y-1} \\ \text{Divide both sides by 2;} \\ x=\frac{\pm\sqrt[]{-5y^2-y-1}}{2} \end{gathered}[/tex][tex]undefined[/tex]On a number line, let point P represent the largest integer value that is less than V380.Let point Q represent the largest integer value less than 54.What is the distance between P and Q?A. 10B. 11C. 12D. 13
We have to find P and Q first.
P is the largest integer that is less than the square root of 380.
P is 19.
Q is the largest number that is less than the square of 54.
Q is 7.
Then the distance between P and Q is |19-7|=12.
Answer: C. 12
Graph v (standard position) and find its magnitude. Show all work.
EXPLANATION
[tex]\mathrm{Computing\: the\: Euclidean\: Length\: of\: a\: vector}\colon\quad \mleft|\mleft(x_1\: ,\: \: \ldots\: ,\: \: x_n\mright)\mright|=\sqrt{\sum_{i=1}^n\left|x_i\right|^2}[/tex][tex]=\sqrt{2^2+5^2}[/tex][tex]=\sqrt{4+5^2}[/tex][tex]=\sqrt{4+25}[/tex][tex]=\sqrt{29}[/tex]Now, we need to graph the vector as shown as follows:
how to solve 4(a+1)=12how to solve 13+2k=5+4khow to solve -4e+28=10ehow to solve -6(4+c)=-66
In this problem, we must solve some linear equations.
1)
[tex]\begin{gathered} 4\cdot(a+1)=12, \\ a+1=\frac{12}{4}, \\ a+1=3, \\ a=3-1, \\ a=2. \end{gathered}[/tex]2)
[tex]\begin{gathered} 13+2k=5+4k, \\ 13-5+2k=4k, \\ 8+2k=4k, \\ 4k-2k=8 \\ 2k=8, \\ k=\frac{8}{2}, \\ k=4. \end{gathered}[/tex]3)
[tex]\begin{gathered} -4e+28=10e, \\ 28=10e+4e, \\ 28=14e, \\ e=\frac{28}{14}, \\ e=2. \end{gathered}[/tex]4)
[tex]\begin{gathered} -6(4+c)=-66, \\ 4+c=\frac{-66}{-6}, \\ 4+c=11, \\ c=11-4, \\ c=7. \end{gathered}[/tex]Answers
• a = 2
,• k = 4
,• e = 2
,• c = 7
Pyramid with the square base. Is this correct? Base=64in^2LA= 112in^2TA=176in^2
The given figures is of square pryamid with the square base
Area of square = side x side
In the given figure, the length of the base of the square = 8in
Area of base of square = 8 x 8
Area of base of square = 64 in²
The lateral area of a right pyramid can be calculated by
multiplying half of the perimeter of the base by the slant
height.
Lateral surface area = 1/2 x Perimeter of the base x slant height
Since, the base of the pryamid is square so, the perimeter for the base pf pryamid = 4side
Perimeter = 4 x side
Perimeter = 4 x 8
Perimeter of the base of pryamid is 32 in
Slant height is given as 7in
Lateral surface area = 1/2 x 7 x 32
LAteral surface area = 7 x 16
Lateral surface area = 112 in²
The total surface area can be calculated by adding base are to the lateral surface area
Total surface area = Lateral surface area + Base area
Total surface area = 112 + 64
Total surface area = 176 in²
Answer:
Area of base of square = 64 in²
Write a value that will make the relation not represent a function
Given:
There are given that the data for x and y are in the form of a table.
Explanation:
According to the concept of function:
The function is not defined when the value of x will be repeated.
That means if the input value is repeated again and again then the given relation will not function.
In the given relation, we can put 7 into the input box.
Final answer:
Hence, the value is 7.
The area of a rectangle is x2 – 8x + 16. The width of therectangle is x – 4. What is the length of the rectangle?-
To answer this question, we need to remember that the area of a rectangle is given by:
[tex]A_{\text{rectangle}}=l\cdot w[/tex]And we have - from the question - that:
[tex]A_{\text{rectangle}}=x^2-8x+16[/tex]And the width of the rectangle is:
[tex]w=x-4[/tex]If we factor the polynomial that represents the area, we need to find two numbers:
• a * b = 16
,• a + b = -8
And both numbers are:
• a = -4
,• b = -4
Since
• -4 * -4 = 16
,• -4 - 4 = -8
Therefore, we can say that:
[tex]x^2-8x+16=(x-4)(x-4)=(x-4)^2[/tex]Therefore:
[tex]l\cdot w=A_{\text{rectangle}}[/tex][tex]l=\frac{A_{rec\tan gle}}{w}[/tex]Then the length of the rectangle is:
[tex]l=\frac{x^2-8x+16}{x-4}=\frac{(x-4)(x-4)}{x-4}\Rightarrow\frac{x-4}{x-4}=1[/tex][tex]l=\frac{(x-4)}{(x-4)}\cdot(x-4)\Rightarrow l=x-4[/tex]In summary, therefore, the length of the rectangle is x - 4.
[tex]l=x-4[/tex][We can check this result if we multiply both values as follows:
[tex]A_{\text{rectangle}}=l\cdot w=(x-4)\cdot(x-4)=(x-4)^2_{}[/tex]And we already know that the area of the rectangle is:
[tex]x^2-8x+16=(x-4)^2[/tex].]
its composition of fractions in pre-calculus.I know how to do these types of questions, im just not sure how u would set it up if there are 2 x's in one of the equations.
Answer:
(f o g)(x) = x
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=\frac{1-x}{x} \\ g(x)=\frac{1}{1+x} \end{gathered}[/tex]The composition (f o g)(x) is obtained below:
[tex]\begin{gathered} (f\circ g)(x)=f\lbrack g(x)\rbrack \\ f(x)=\frac{1-x}{x}\implies f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)} \end{gathered}[/tex]Substitute g(x) into the expression and simplify:
[tex]\begin{gathered} f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)}=\lbrack1-g(x)\rbrack\div g(x) \\ =(1-\frac{1}{1+x})\div(\frac{1}{1+x}) \\ \text{ Take the LCM in the first bracket} \\ =\frac{1(1+x)-1}{1+x}\div\frac{1}{1+x}\text{ } \\ \text{Open the bracket} \\ =\frac{1+x-1}{1+x}\div\frac{1}{1+x}\text{ } \\ =\frac{x}{1+x}\times\frac{1+x}{1}\text{ } \\ =x \end{gathered}[/tex]Therefore, the composition (f o g)(x) is x.
Eight less than a number n is at least 10
Answer:
n - 8 ≥ 10
n ≥ 18
Step-by-step explanation:
Hello!
8 less than the number n can be represented as n - 8.
To be atleast 10, we can have values greater than 10 and equal to 10, but cannot be less than 10 . We can use the ≥ symbol to represent this.
The inequality would be n - 8 ≥ 10
Solving for n:n - 8 ≥ 10n ≥ 18n has to be greater than or equal to 18
How do you solve this??
A mathematical statement comprehended as an equation exists created up of two expressions joined together by the equal sign.
If the equation be 12 - 2x = x - 3 then the value of x = 5.
What is meant by an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
A mathematical phrase with two equal sides and an equal sign is called an equation. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let the equation be 12 - 2x = x - 3
Subtract 12 from both sides
12 - 2x - 12 = x - 3 - 12
Simplifying the above equation, we get
-2x = x - 15
Subtract x from both sides
-2x - x = x - 15 - x
Simplifying the above equation, we get
-3x = -15
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-15}{-3}[/tex]
Therefore, the value of x = 5.
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Add the rational expression as indicated be sure to express your answer in simplest form. By inspection, the least common denominator of the given factor is
Notice that the least common denominator is 9*2=18, therefore:
[tex]\begin{gathered} \frac{x-3}{9}+\frac{x+7}{2}=\frac{2(x-3)}{9\cdot2}+\frac{9(x+7)}{9\cdot2}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6}{18}+\frac{9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6+9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.} \end{gathered}[/tex]Answer:
[tex]\frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.}[/tex]use the generic rectangle 3x-8)² and -7x⁴(3x-2) what's the product and sum?
In this case the answer is very simple .
Step 01:
Data:
eq1. (3x - 8)²
eq2. -7x⁴(3x-2)
Step 02:
Sum.
eq.1 + eq.2
(3x - 8)² + (-7x⁴(3x-2))
(9x² - 2*3x*8 - 64) + (-21x⁴ - 14x⁴)
9x² -
A sample of 7 students was taken to see how many pencils they were carrying.2, 3, 2, 5, 7, 1, 41. Calculate the sample mean.2. Calculate the standard deviation.
Sample mean = 3.43
sample standard deviation = 2.07
Explanation:
Given: 2, 3, 2, 5, 7, 1, 4
Total numbers = 7
1) Sample mean is calculated by finding the average of the data set
[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]2) We have sample standard deviation and population standard deviation.
SInce the question asked for sample mean, we will be calculating sample standard deviation.
Standard deviation is calculated as:
[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]
Graph the inequality on a number line
Lucky Champ owes $209.10 interest on a 6% loan he took out on his March 17 birthday to upgrade an oven in his Irish restaurant, Lucky's Pub and Grub. The loan is due on August 17. What is the principal? (Use 360 days a year.)
Based on the interest owed on the loan and the date that the loan is due and when Lucky Champ took it, the principal for the loan is $8,200.
How to find the principal?First, find the period of the loan:
= 14 days in March + 30 + 31 + 30 + 31 + 17 days in August
= 153 days
The interest can be found by the formula:
= Principal x Interest rate x Period
The Principal can therefore be found by the formula:
= Interest owed x Number of days in year / Number of days x 100 / 6
= 209.10 x 360 / 153 x 100 / 6
= $8,200
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4/7 X 1/2 = in fraction
Consider the given expression,
[tex]P=\frac{4}{7}\times\frac{1}{2}[/tex]The product of fractions is obtained in the form of a fraction whose numberator is the product of numerators of fractions, and the denominator of the product is the product of denominators of the given fractions,
[tex]\begin{gathered} P=\frac{4\times1}{7\times2} \\ P=\frac{4}{14} \end{gathered}[/tex]Thus, the product of the given fractions is 4/14 .
Help me please I've watched like five videos and still don't get it!
14)
Given data:
The given triangle.
As all the sides of the triangle are equal, it means all the angles are equal. The expression for the angle sum property of the triiangle is,
[tex]\begin{gathered} x+x+x=180^{\circ} \\ 3x=180^{\circ} \\ x=60^{\circ} \end{gathered}[/tex]In the given triangle each angle is 60 degree, so it is an acute angle triangle.
Thus, the given triangle is an acute angle triangle, so first option is correct.
15)
The all sides and all angles of the triangle are equal.
Thus, the given triange is an equilateral triangle, so third option is correct.
Which graph represents 2x + 3y < 6?Choose 1 answer:
Given: An inequality
[tex]2x+3y<6[/tex]Required: To determine the graph of the inequality.
Explanation: The inequality represent an area either inside or outside a line determined by repl
Please show formula and explain work in 6th grade format
The surface area of a pyramid is given as:
[tex]SA=\frac{1}{2}pl+B[/tex]where p is the perimeter of the base, l is the slant height and B is the area of the base.
In this case the slant height is 4 in.
Now, since the base is a square which sides that has length 5 in. then the perimeter is:
[tex]p=4\cdot5=20[/tex]The area of the base is the length of the side squared, then we have:
[tex]B=5^2=25[/tex]Once we know the values we plug them in the formula, then we have:
[tex]\begin{gathered} SA=\frac{1}{2}(20)(4)+25 \\ SA=40+25 \\ SA=65 \end{gathered}[/tex]Therefore the surface area is 65 squared inches.
A manufacturer pays its assembly line workers $11.06 per hour. In addition, workers receive a piece of work rate of $0.34 per unit produced. Write a linear equation for the hourly wages W in terms of the number of units x produced per hour. Linear equation: W = _______ What is the hourly wage for Mike, who produces 17 units in one hour? Mike’s wage = _________
Let's assume the following variables.
x = number of units produced
It is stated in the problem that for every unit produced, there is an additional wage of $0.34. Hence, on top of $11.06 per hour wage, there will be an additional of $0.34x per hour. In equation, we have wage per hour:
[tex]W=11.06+0.34x[/tex]If Mike was able to produce 17 units, our x here is 17. Let's plug this value to the formula.
[tex]W=11.06+0.34(17)[/tex]Then, solve.
[tex]\begin{gathered} W=11.06+5.78 \\ W=16.84 \end{gathered}[/tex]Therefore, Mike's hourly wage is $16.84.
х3,2y=x?(x, y)00(0,0)2.4(2, 4)For which value of x is the row in the table of values incorrect?3The function is the quadratic function y = -x?4366를18(3,6)(5,18 )5
Since the given equation is
[tex]y=\frac{3}{4}x^2[/tex]If x = 0, then
[tex]y=\frac{3}{4}(0)^2=0[/tex]Then x = 0 is correct because it gives the same value of y in the table
If x = 2
[tex]\begin{gathered} y=\frac{3}{4}(2)^2 \\ y=\frac{3}{4}(4) \\ y=3 \end{gathered}[/tex]Since the value of y in the table is 4
Then x = 2 is incorrect
What is the value of 3/8 dividend by 9/10
A) 3
B 5/12
C 27/80
D 2/3
Answer:
B 5/12 (im stupi d)
Step-by-step explanation:
(3/8)/(9/10) = (3/8) * (10/9) = 5/12
Answer:
B) [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Apply the fractions rule a/b ÷c/b = a/b × d/c
= 3/8 x 10/9
Multiply fractions a/b x c/d = [tex]\frac{axc}{b x d}[/tex]
Multiply the numbers: 3 x 10 = 30
= 3/10 8 x 9
Multiply the numbers: 8 x 9 = 72
= 30/72
Cancel the common factor: 6
5/12
