The value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
It is given to us that -
[tex]P(-c\leq Z\leq c)=0.9127[/tex] is true
It is also given that Z follows the standard normal distribution.
We have to find out the value of c.
Since Z follows the standard normal distribution, so we can say that
Z ∼ N(0,1)
To find out c,
[tex]P(-c\leq Z\leq c)=0.9127\\= > P(Z\leq c)-P(Z\leq -c)=0.9127\\[/tex]
Since there is a symmetric z-distribution, the above equation can be represented as -
[tex][1-P(Z\leq -c)]-P(Z\leq -c) = 0.9127\\= > 1-P(Z\leq -c) - P(Z\leq -c) = 0.9127\\= > 1-2P(Z\leq -c)=0.9127\\= > 2P(Z\leq -c)=0.0873\\= > P(Z\leq -c)=0.04365[/tex]
=> -c ≈ 0.0873 (Using online calculator)
Therefore, the value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
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Answer:
The value of c such that is true is 0.0873 where Z follows the standard normal distribution.
Step-by-step explanation:
what is the dependent variable to the following equationy=3x+9
hello
to solve this question, let's identify the independent an dependent variable.
*independent variable: this is the variable that can stand alone on it own. It is usually equated with the rest of the equation.
in this question, the independent variable is y
*dependent variable: this is the variable that can't stand on it's own and also depends on the other side of the equation.
in this question, the dependent variable is x
One serving of mikes crackers has 150 calories and a mass of 30 grams. how many calories are in y of the crackers
one serving has 150 calories and a mass of 30 g
1 gram= 150/30 = 5 calories
so y grams = y x 5 calories = 5y calories
find the solution of this system of equations2x-2y=149x+4y=37
2x-2y=14
9x+4y=37
Multiply the first equation by 2, and then add both :
4x-4y=28
+
9x+4y=37
_______
13x = 65
Divide both sides of the equation by 13
13x/13 = 65/13
x= 5
Replace x on any equation and solve for y:
2x-2y=14
2(5)-2y=14
10-2y= 14
Subtract 10 from both sides:
10-10-2y= 14-10
-2y= 4
Divide both sides by -2
-2y/-2 =4/-2
y= -2
Solution:
x=5
y= -2
9000 Employees 24 hours a day 365 days a week how many man hours a year
Answer: 2096 work hours per year
Which relations are functions?Select Function or Not a function for each graph. FunctionNot a functionGraph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the origin and the points begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair 2 comma 4 end ordered pair.Function –Not a function –The graph of a parabola on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is located at begin ordered pair 1 comma 0 end ordered pair. The parabola opens upward. It passes through the vertical axis at begin ordered pair 0 comma 1 end ordered pair. It passes through begin ordered pair 2 comma 1 end ordered pair.Function –Not a function –An absolute value function graphed on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is at the origin. The V-shaped graph passes through the points begin ordered pair 1 comma 1 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair.Function –Not a function –A circle on a coordinate plane centered at the origin, begin ordered pair 0 comma 0 end ordered pair. The circle passes through points begin ordered pair negative 2 comma 0 end ordered pair, begin ordered pair 0 comma negative 2 end ordered pair, begin ordered pair 2 comma 0 end ordered pair, and begin ordered pair 0 comma 2 end ordered pair.Function –Not a function –
SOLUTION
To identify or determine which relation in the graph is a function, we use the vertical line test.
The vertical line test explains that If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x-value has more than one output. A function has only one output value for each input value.
Hence, from the explanation above, we cam see that
Graph 1 is a Function
Graph 2 is a Function
Using similar approach
Graph 3 is not a function
Graph 4 is not a function
The hypotenuse of an isosceles right triangle is 6cm longer than either of its legs. Note that an Isosceles right triangle is a right triangle whose legs are the same length, find the exact length of its legs and it’s hypotenuse
We know by the pythagorean theorem that
We know that the length of the hypotenuse squared will be equal to the sum of the legs squared. The problem says that the legs have the exact same length and the hypotenuse is 6cm longer, so we can write
Where "a" is the leg length, see that we can apply the pythagorean theorem here, and it will be
[tex]a^2+a^2=(a+6)^2[/tex]See that now c = a + 6, and b = a.
We can simplify that expression
[tex]2a^2=(a+6)^2[/tex]We know that
[tex](a+6)^2=a^2+12a+36[/tex]Therefore our equation will be
[tex]2a^2=a^2+12a+36[/tex]Now we pass all the terms for one side and we will have a quadratic equation
[tex]-a^2+12a+36=0[/tex]We can use the formula for the quadratic equation and find out the solutions
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Using it
[tex]\frac{-12\pm\sqrt[]{12^2-4\cdot(-1)\cdot36}}{2\cdot(-1)_{}}[/tex]Now we can just do all the calculus
[tex]\frac{-12\pm\sqrt[]{144^{}+144}}{-2_{}}=\frac{12\pm\sqrt[]{2\cdot12^2}}{2}=\frac{12\pm12\sqrt[]{2}}{2}[/tex]Then the solution are
[tex]\begin{cases}a_1=6+6\sqrt[]{2} \\ a_2=6-6\sqrt[]{6}\end{cases}[/tex]Even though we have two solution, see that the second one is negative, and we can't have negative length! Then the length of its legs will be
[tex]a=6+6\sqrt[]{6}[/tex]And the hypotenuse will be a + 6, then
[tex]h=6+6+6\sqrt[]{6}=12+\sqrt[]{6}[/tex]Therefore, the legs and the hypotenuse length is
[tex]\begin{gathered} l=6+\sqrt[]{6} \\ h=12+6\sqrt[]{6} \end{gathered}[/tex]We can write it approximately as
[tex]\begin{gathered} l=14.485\text{ cm} \\ h=20.485\text{ cm} \end{gathered}[/tex]If we want a more rough approximation we can say it's
[tex]\begin{gathered} l=14.5\text{ cm} \\ h=20.5\text{ cm} \end{gathered}[/tex]The dancer at (4,1) needs hair gel. She moved to the right on a slope of 8. Where can you deliver her hair gel? Will you please provide a graph and a written detailed explanation? Thank you!
It is given that the dancer is at the point (4,1), and then moved to the right on a slope of 8.
It is required to find the point she can be located by showing a graph with a detailed explanation.
Recall that the slope is the measure of the steepness of a line calculated by dividing the vertical change by the horizontal change.
Since the slope is given as 8, and this can be written as 8/1. It follows that the vertical change is 8 and the horizontal change is 1.
To find the new point add 1 to the x-coordinate (which represents the horizontal) and 8 to the y-coordinate (which represents the vertical):
[tex](4,1)\rightarrow(4+1,1+8)=(5,9)[/tex]Hence, the new position is at the point (5,9).
This is illustrated in the graph below:
The gel can be delivered at (5,9) as shown above.
You and a friend go to Efren’s Tacos and Burritos for lunch. You order 2 tacos and 2 burritos for a total of $9.00. Your friend orders 1 taco and 3 burritos for a total of $10.50. Create a system of equations and solve for how much each burrito costs and how much each taco costs.
Use b as your variable for burritos and t as your variable for tacos.
PLEASE SOMEONE ANSWER THIS FAST
Each burrito costs $3 and each taco costs $1.50.
How to calculate the equation?Let b = variable for burrito
Let t = variable for tacos.
The equation based on the information will be illustrated as:
t + 3b = 10.50 .... i
2b + 2t = 9 ..... ii
From equation i, t = 10.50 - 3b. Put this into equation ii
2b + 2t = 9 .
2b + 2(10.50 - 3b) = 9
2b + 21 - 6b = 9
Collect like terms
4b = 12
b = 12/4
b = 3
Burrito = $3
Since t + 3b = 10.50
t + 3(3) = 10.50
t + 9 = 10.50
t = 10.50 - 9
t = 1.50
Taco= $1.50
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Instructions: Create a table of values for the given function.
Given the function:
f(x) = 4x - 4
We re asked to create a table of values for thhe above function.
In order to create the tabe of value, we will use the x values give n in the table to replace the value of x in the function.
When x = -2
f(x) = 4(-2) - 4
= -8 - 4
= -12
When x = -1
f(x) 4(-1() - 4
= -4 - 4
= -8
When x = 0
f(x) = 4(0) - 4
= 0 - 4
= -4
When x = 1
f(x) = 4(1) - 4
= 4 - 4
= 0
When x = 2
f(x) = 4(2) - 4
= 8 - 4
= 4
So, let's complete the table:
x y
-2 -12
-1 -8
0 -4
1 0
2 4
ASAP Please help and ThankyouThis graph shows how the total distance jack has walked depends on the number of trips he has made to school. What is the rate of change?
we will take two points on the line,
first is (0,2) and other is (1, 4)
the rate of change will be the slope of the line,
[tex]\begin{gathered} m=\frac{4-2}{1-0} \\ m=\frac{2}{1}=2 \end{gathered}[/tex]so the rate of the change is 2 km per trip
so the answer is 2
Does the quadratic functionf(x) = 4x2 – 12x + 9 have one,two, or no real zeros? Utilize thequadratic formula to determinethe answer[?] real zero(s)-b Vb2 - 4acRemember the quadratic formula: x =
SOLUTION
Step1: Write out the equation
[tex]y=-2x^2-4x+2[/tex]Compare the equation with the general form of a quadratic equation
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{then } \\ a=-2,b=-4,c=2 \end{gathered}[/tex]Step2 Write out the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step3: Substitute the parameters in step1
Translate the sentences into an algebraic inequality.A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to book the bus.
ANSWER
[tex]\text{15 }\leq\text{ x }\leq55[/tex]EXPLANATION
The tour bus can seat 55 passengers.
A minimum of 15 people must register for the tour to book the bus.
This means that the number of people that must register for the tour must be greater than or equal to 15 and less than or equal to 55.
Let the number of people that must register be x.
Then we have that the inequality that represents the situation is:
[tex]\begin{gathered} x\ge\text{ 15 and x }\leq\text{ 55} \\ \Rightarrow\text{ 15 }\leq\text{ x }\leq55 \end{gathered}[/tex]That is the inequality.
4. Which of the following expressions will have the same value as the expression below? -7-(-5)A. -7+(-5)B. -7-5C. 7+(-5)D. -7+5
1) Let's operate this expression -7 -( -5)
-7 -( -5) The minus before the parentheses work as -1 x (-5)
-7 +5
-2
2) Examining each expression
a) -7+(-5) = -7 -5 = -12
b) -7-5= -12
c) 7-5 = 2
d) -7+5 = -2
3) So according to the options, the answer is D
Evaluate the function for the given value of x.p(x) = x2-9x, q(X) = VX-6,(p. q)(x) = ?
The functions are:
[tex]\begin{gathered} p(x)=x^2-9x \\ q(x)=\sqrt[]{x-6} \end{gathered}[/tex]So the product (p*q) is
[tex](p\cdot q)(x)=(x^2-9x)(\sqrt[]{x-6})[/tex]So the solution is is B)
In the quadratic formula the expression b^2-4ac is called the _____1 maximum value 2 discriminant3 minimum value
ANSWER :
Discriminant
EXPLANATION :
b^2 - 4ac in quadratic formula determines if the roots are real or imaginary.
It is called discriminant.
55 pointsWhen the equation log. ( VnUn = 3 is solved for n in terms of a, where a > 0,a # 1, the resulting equation isn=adn = 03ооооn = 9n = 26Previous
please wait the question is downloading
the answer is
n=a^6-5ln+4l<15 true or false
So, for values lesser than -1 and greater than -7 this inequality is true.
In this inequality let's work applying the Absolute Value properties
1) -5ln+4l<15 Dividing both sides by 5
-|n+4|<3
|n+4|>-3
2) Applying Absolute value properties
|n+4|>-3
|n+4|>-3
n+4-4>-4-3
n>-4-3
n>-7
|n+4|>3
n+4>3
n+4-4>3-4
n>-1
3) So n < -1 and >-7
So for values lesser than -1 and greater than -7 this inequality is true.
what is the distance between points (5,2) and (1,-3) on a coordinate plane?A 3B 4.1C 8.5D 6.4
We are asked to find the distance between the following two points
[tex](5,2)\: and\: (1,-3)[/tex]Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex][tex]\begin{gathered} \mleft(x_1,y_1\mright)=\mleft(5,2\mright) \\ (x_2,y_2_{})=(1,-3) \end{gathered}[/tex]Let us substitute the given points into the above distance formula
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1_{}-5_{}})^2+({-3_{}-2})^2} \\ d=\sqrt[]{({-4})^2+({-5})^2} \\ d=\sqrt[]{16^{}+25^{}} \\ d=\sqrt[]{41} \\ d=6.4 \end{gathered}[/tex]Therefore, the distance between the given two points is 6.4
Option D is the correct answer.
(1/4) raised to the power of (x-2)=16I'll upload a picture
Answer
x = 0
Explanation
[tex]\begin{gathered} (\frac{1}{4})^{x-2}=16 \\ 4^{-1(x-2)}=4^2 \\ 4^{-x-2}=4^2 \\ \text{Equate both sides of the equation} \\ -x+2=2 \\ -x=2-2 \\ -x=0 \\ x=0 \end{gathered}[/tex]1) In 2014, the percentage of households that owned a 4K TV was found to be 18%. Using a sample of 300 households in which 60 of them owned a 4K TV, do we have sufficient evidence that the percentage of households with a 4K TV has increased? Use a level of significance of 0.10.
Hello there. To solve this question, we need to calculate the percentage of households that owns a 4K TV with the values given in the sample and compare with the other percentage to see if the value has increased.
Using that sample of 300 households, in which 60 of them owns a 4K TV, we get that the percentage will be calculated by the ratio:
60/300
Simplify the fraction by a factor of 60
1/5
Multiply it by 100%
20%, equal to 0.20
In 2014, we had that percentage being equal to 18%, which is equal to 0.18
So, we do have sufficient evidence that the percentage of households satifying this situation have increased with the time.
Leann determines the volume of the cylinder shown using the formula V=Bh.
We have that the base of the cylinder is a circle, and the area of a circle can be calculated with the following equation:
[tex]B=\pi\cdot r^2[/tex]In this case, we have the following:
[tex]\begin{gathered} \pi=3.14 \\ r=\frac{d}{2}=\frac{6}{2}=3 \\ \Rightarrow B=(3.14)(3)^2=(3.14)(3)(3) \end{gathered}[/tex]therefore, the area of the base is B=(3.14)(3)(3) = 28.26 cm^2
How many baseballs with a diameter of 2.90inches, can fit into a box that is 48in x 40in x36in?
Answer:
5413 baseballs
Explanation:
Dimensions of the box = 48in x 40in x 36in.
The diameter of one baseball = 2.90 inches
Radius = Diameter ÷ 2 = 2.90 ÷ 2 =1.45 Inches
First, we find the volume of one of the baseball.
The baseball is in the shape of a sphere and:
[tex]\text{Volume of a Sphere}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of one baseball will be:
[tex]\begin{gathered} =\frac{4}{3}\times\pi\times1.45^3 \\ =12.77in^3 \end{gathered}[/tex]Next, we find the volume of the box.
[tex]\begin{gathered} \text{Volume of the box}=48\times40\times36 \\ =69120in\text{.}^3 \end{gathered}[/tex]Therefore, the number of baseballs that will fit into the box will be:
[tex]\begin{gathered} \frac{\text{Volume of the box}}{Volume\text{ of one baseball}}=\frac{69120}{12.77}=5412.7 \\ \approx5413 \end{gathered}[/tex]Econ The area of a square is 36 square meters. What is the length (in meters) of one side of the square
We have the following equation of the area of a square:
[tex]A=s^2[/tex]where s is the length of the side.
In this case, we have that the area is 36 square meters, then:
[tex]\begin{gathered} A=36m^2=s^2 \\ \Rightarrow s^2=36 \end{gathered}[/tex]if we apply the square root on both sides we get:
[tex]\begin{gathered} \sqrt[]{s^2}=\sqrt[]{36}=6 \\ \Rightarrow s=6 \end{gathered}[/tex]therefore, the measure of the side of the square is 6 meters
2. Ifa 28% tip is left on a restaurant bill of $80, find the total amount of the bill including
To find 28% of $80, we have to first convert 28% to decimal, then multiply $80 with it.
28% = 28/100 = 0.28
Now,
[tex]0.28\times80=\$22.4[/tex]The total amount of bill INCLUDING the tip is the total bill added to the tip amount. That is:
[tex]80+22.4=\$102.40[/tex]Total Amount:$102.40
Round .00000572. Using single digit and power of 10
Given that
There is a number and we have to round it using the single digit and in powers of 10.
Explanation -
Whenever we convert a decimal number into powers of 10.
The power of 10 is always equal to the negative number of digits after the decimal.
Then, the number 0.00000572 can be written as0
[tex]0.00000572=5.72\times10^{-6}[/tex]Now we have to round off it to a single digit.
Then,
[tex]5.72\times10^{-6}\approx6\times10^{-6}[/tex]Final answer -
Therefore the final answer is 6 x 10^(-6)35 06286 rounded to the nearest ten thousandth is
35. 06 286 = 35.0629
to a certain meeting room a college charge a reservation fee of $37 and a ln additional fee of $9.40 per hour. the math club wants to spend less than $ 93.40 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room. use t for the number of hours the meeting room is rented and solve your inequality for t
For the information given in the statement, you have the inequality:
[tex]\text{ \$37+\$9.40t < \$93.40}[/tex]Now, to solve the inequality, subtract $37 from both sides of the inequality.
[tex]\begin{gathered} \text{ \$37+\$9.40t -\$37< \$93.40 - \$37} \\ \text{ \$9.40t < \$}56.4 \end{gathered}[/tex]Now, divide by $9.40 into both sides of the inequality
[tex]\begin{gathered} \text{ \$9.40t < \$}56.4 \\ \frac{\text{ \$9.40t }}{\text{ \$9.40}}\text{< }\frac{\text{\$}56.4}{\text{ \$9.40}} \\ t<6 \end{gathered}[/tex]Therefore, the math club could rent the meeting room for a maximum of 6 hours.
Choose all properties that were used to simplify the following problem:
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The property used in this problem are
commutative property of additionassociative property of additionadditive inverseadditive identityProperty of numbers.
We know that, there are four basic properties of numbers.
They are commutative, associative, distributive, and identity.
Given,
Here we have the problem
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
Now, we need to identify all properties that were used to simplify the problem.
In the first step of the problem is,
[38 + 677] + (-38)
We have used the commutative property of addition to interchange the given numbers in the brackets,
[677 + 38] + (-38)
Now, we have to use the associative property of addition to group the numbers,
677 + [38 + (-38)]
Then we have to use the additive inverse, to get the value of brackets,
677 + 0
Finally we have to use the additive identity to get the result.
677
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Find the total value of the investment after the time given: $36,000 at 13.7% compounded semiannually for 2 years
A = P ( 1 + r/n ) ^ nt
P is the principle which is 36000
r is the rate which is 13.7 % or .137 in decimal form
n is the number of time per year, semi annual means 2 times per year
t is the time = 2
A = 36000( 1 + .137/2) ^ (2*2)
36000( 1 + .137/2) ^ (4)
What is 505 divided by 2, if there is a remainder, please say it in your answer or explanation.
Answer:
252,5 or 2,525 rounded.
Step-by-step explanation:
Rounding explanation:
2525_
You rounded to the nearest one's place. The 5 in the ones place rounds down to 5, or stays the same because the digit to the right in the tenth place is _.
2,525
When the digit to the right is less than 5 we round toward 0.2525 was rounded down toward zero to 2,525