2 * 10^4 = 2 * 10000 = 20,000
4 * 10^6 = 4 * 1000000 = 4,000,000
4,000,000/20,000 = 200
Therefore, 4 * 10^6 is 200 times 2 * 10^4
Given a standard normal curve, find the area under the curve between z =1.40 and z =2.13.
Given:
z = 1.40 and z = 2.13
Let's find the area under the standard normal curve.
Let's find the score using the standard normal distribution table:
NORMSDIST(1.40) = 0.9192
NORMSDIST(2.13) = 0.9834
To find the area between them, we have:
P(1.40 < Z < 2.13) = P(Z<2.13) - P(Z<1.40) = 0.9834 - 0.9192 = 0.0642
Therefore, the area under the curve between z=1.40 and z=2.13 is 0.0642
ANSWER:
0.0642
what is polynomial define on the basis of degree and terms
Detailed Answer :-
Based on the Degree :
• A polynomial having degree 0 is called a constant polynomial.
• A polynomial having degree 1 is called a linear polynomial.
• A polynomial having degree 2 is called a quadratic polynomial.
• A polynomial having degree 3 is called a cubic polynomial.
• A polynomial having degree 4 is called a bi-quadratic polynomial.
Based on the Number of Terms :
• One term - Monomial
• Two terms - Binomial
• Three terms - Trinomial
• Four terms - Quadrinomial
All of these are generally called POLYNOMIALS.
log(x) + log(x + 3) = 7
Answer:
[tex]x=3160.778016...[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log(x)+\log(x+3)=7[/tex]
[tex]\textsf{Apply the product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log(x(x+3))=7[/tex]
[tex]\implies \log(x^2+3x)=7[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^2+3x=10^7[/tex]
[tex]\implies x^2+3x-10000000=0[/tex]
Solve the quadratic equation by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=3,\quad c=-10000000[/tex]
Substitute the values of a, b and c into the quadratic formula:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(-10000000)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{9+40000000}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{40000009}}{2}[/tex]
[tex]\implies x=3160.778016..., \quad x=-3163.778016...[/tex]
As logs of negative numbers cannot be taken, the only valid solution is:
[tex]\boxed{x=3160.778016...}[/tex]
I’m not sure how to figure this out.What is 8% of 4000?
8% of 4000 express as;
[tex]\begin{gathered} \text{ 8\% of 4000=}\frac{8\times4000}{100} \\ \text{8\% of 4000=320} \end{gathered}[/tex]Thus, 8% of 4000 is 320
Answer : 320
...
-10 x is greater than or equal to 2x
We need to solve the following inequality:
[tex]-10\text{ }\ge2x[/tex]We need to isolate the "x" variable, when we do that the number that is multiplying it should go to the other side with its inverse operation, which is division.
[tex]\begin{gathered} \frac{-10}{2}\ge x \\ -5\ge x \end{gathered}[/tex]Now we need to flip the expression, so the variable is isolated on the left side. Since this is an inequality we also need to flip the inequality signal. This is done below.
[tex]x\leq-5[/tex]For the expression to be true x must be less or equal to -5.
Find the area and the circumference (or perimeter) of each of the following. (a)a penny; (b) anickel; (c) a dime; (d) a quarter, (e) a half-dollar; (f) a silver dollar; (g) a Sacajawea dollar; (h) adollar bill; and (i) one face of the pyramid on the back of a $1 bill.
You use this for the coins
Area of a circle:
[tex]A=\pi\cdot r^2[/tex]r is the radius and it can be obtaided more easily if you measure the diameter of the circle and then divide it into 2.
Circunference or perimeter of a circle:
[tex]C=2\cdot\pi\cdot r[/tex]--------------------------------------------
You use this for the bills:
Aera of a rectangle:
[tex]A=l\cdot w[/tex]Perimeter of a rectangle:
[tex]P=2l+2w[/tex]------------------------
The face a pyramid has the shape of a trianlge:
Area of a triangle:
[tex]A=\frac{1}{2}b\cdot h[/tex]Perimeter of a triangle:
[tex]P=b+a+a[/tex]Hello could you please help me with question number five?
Question #5
Given:
The number of people who own computers has increased 23.2% annually since 1990
In 1990: the number of people who own computers = half a million
We will predict the number of people in 2015
We will use the following formula:
[tex]P(t)=P_o\cdot(1+r)^t[/tex]Where: (r) is the ratio of increasing = 23.2% = 0.232
And (t) the number of years after 1990
And P₀ is the initial value of the number of people
P(t) will be the number of people after (t) years
To predict the number of people in 2015
t = 2015 - 1990 = 25 years
so,
[tex]\begin{gathered} P=0.5\cdot(1+0.232)^{15} \\ P=0.5\cdot1.232^{15}\approx11.43\text{ millions} \end{gathered}[/tex]So, the answer will be:
The estimated number of people = 11.43 million
You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?
Answer:
y=3^x
Explanation:
The expected payments (in cents) beginning from July 1 are given below:
[tex]3,9,27,81,\cdots[/tex]Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.
We can rewrite the payment as a power of 3 as follows:
[tex]3^1,3^2,3^3,3^4,\cdots[/tex]Therefore, the equation will help you determine how much money you will make in July will be:
[tex]y=3^x[/tex]The first option is correct.
The Following to wait table shows the number of student of the school who have a cell phone and or part-time job:
Explanation
in the column we have
-have cell phones
-do not have cell phones
-total
and
in the other side.
-have a part time job
-do not have part time job,
so to know the number of students whoh fit both conditions ( have a cell phone and have a part time job) we need to find the cell where both intersect each other
hence, the answer is
[tex]2)40[/tex]I hope this helps you
What is the domain of F
If the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] then the domain of the function exists
[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]
What is meant by domain of a function?The collection of all potential inputs for a function is its domain.
Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Let the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]
Domain of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] :
[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]
Range of [tex]$\frac{x^3-3 x+1}{8 x-5}:\left[\begin{array}{cc}\text { Solution: } & -\infty < f(x) < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
Axis interception points of [tex]$\frac{x^3-3 x+1}{8 x-5}[/tex]
X Intercepts: [tex]$(0.34729 \ldots, 0),(1.53208 \ldots, 0)$[/tex], [tex]$(-1.87938 \ldots, 0)$[/tex],
Y Intercepts: [tex]$\left(0,-\frac{1}{5}\right)$[/tex]
Asymptotes of [tex]$\frac{x^3-3 x+1}{8 x-5}: \quad$[/tex]
Vertical: [tex]$x=\frac{5}{8}$[/tex]
Extreme Points of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]
Minimum [tex]$(-0.54351 \ldots,-0.26422 \ldots)$[/tex]
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x Michael uses synthetic division to divide f(x) by g(x), his last line of work 0/3is shown. How would he write his answer of f(x) divided by g(x). *7 0 24 0 0
It's important to know that synthetic division gives a polynomial as a result.
Michael obtained 7 0 24 0 0. We just need to add variables to it. As you can observe, there are 5 terms, that means the polynomial is grade 4.
[tex]7x^4+0x^3+24x^2+0x+0[/tex]Therefore, the resulting polynomial is
[tex]7x^4+24x^2[/tex]The derivative of tan(ln(t)) is?
Answer: The derivative of tan(t) with respect to t is sec2(t) sec 2 ( t ) .
Step-by-step explanation:
hope this helps
draw the image of quadrilateral ABCD under a translation by 1 unit to the right and 6 units up
Assuming any quadrilateral:
A(-2, -1)
B(-1, -4)
C(-4, -6)
D(-5, -3)
Use < or > to write a true sentence. Show your work in the lining up decimals and adding zeroes8.41 8.051
8.41 > 8.051
the digit after the decimal point is greater on 8.41 (4) than on 8.051 (0)
On Saturday, 3 families with 4 people in each family went to a movie. Each person bought 2 snacks. Which equation can be used to find how many total snacks the families bought?
Answer:
Step-by-step explanation:3x4=12x2
Find the lateral area and the surface area of the right cone. Round your answer to the nearest hundredth
The lateral area of a cone is the area of the lateral surface, except the base.
The surface area of a cone is the area of all its surface, which is the lateral side PLUS the base.
The lateral area is given by the formula >>>
[tex]LA=\pi rl[/tex]The surface area is given by the formula >>>
[tex]SA=\pi r^2+\pi rl[/tex]Given
r = 10 cm
h = 24 cm
Let's find l,
[tex]\begin{gathered} r^2+h^2=l^2 \\ 10^2+24^2=l^2 \\ l=\sqrt[]{10^2+24^2} \\ l=26 \end{gathered}[/tex]Let's find the lateral area and the surface area >>>
Lateral Area =
[tex]\begin{gathered} LA=\pi rl \\ LA=\pi(10)(26) \\ LA=260\pi \\ LA=816.81\text{ sq. cm.} \end{gathered}[/tex]Surface Area =
[tex]\begin{gathered} SA=\pi r^2+\pi rl \\ SA=\pi(10)^2+260\pi \\ SA=100\pi+260\pi \\ SA=360\pi \\ SA=1130.97\text{ sq. cm.} \end{gathered}[/tex]A spinner has eight = sections, five of which are gray and red with your blue. The Spinners spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray.
The probability that the first spin lands on blue and the second spin lands on gray is 15 / 56.
What is probability?Probability is the likelihood that an event will happen or take place.
The spinner has eight = sections, five of which are gray and red with your blue.
Probability that the first spin lands on blue = 8
(8 - 5)/8 = 3/8
The probability of landing of gray is 5/7 for the second time.
Therefore, the probability will be:
= 3/8 × 5/7
= 15 / 56
This illustrates the concept of probability.
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Find the midpoint of the line segment IJ where I (3,-9) and J (-10,-5)
Answer:
M (-7/2, -7)
Explanation:
Given the coordinates as I(3, - 9) and J(-10, -5), we can go ahead and determine the midpoint of the line segment IJ using the midpoint formula stated below;
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So we have that x1 = 3, x2 = -10, y1 = -9, and y2 = -5.
Let's go ahead and substitute the above values into our formula and simplify;
[tex]\begin{gathered} M\lbrack\frac{3+(-10)}{2},\frac{-9+(-5)}{2}\rbrack \\ =M(\frac{3-10}{2},\frac{-9-5}{2}) \\ =M(-\frac{7}{2},\frac{-14}{2}) \\ =M(-\frac{7}{2},-7) \end{gathered}[/tex]Christi earns $21 per hour working as a receptionist. If she works 19 hours per week, what is her weekly wage? A) $250 B) $299 C) $350 D) $399
Since Christi earns $21 per hour, to find how much she earns by working 19 hours per week we need to multiply the hourly wage by the number of hours she works in a week:
[tex]21\times19=399[/tex]Her weekly wage is $399
Answer: D) $399
the cash register do ducks $250 from a $25 Coffee Cafe gift card for every medium coffee with a customer buys an equation is written to calculate the total amount on the gift card what is the meaning of the Y intercept in the equation
The equation can be represented by
y= 25 - 2.5x
by comaprison with y = mx + c
c = 25 ( note tha c means y-intercept)
This 25 represents the initial value of the gift card
The correct answer is option d
Solve the following system algebraically. y= x2 - 9x + 18 y = x - 3
we have
y=x^2-9x+18 -----> equation A
y=x-3 ------> equation B
Solve the system of equations
substitute equation B in equation A
x^2-9x+18=x-3
x^2-9x+18-x+3=0
x^2-10x+21=0
Solve the quadratic equation using the formula
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a}[/tex]we have
a=1
b=-10
c=21
substitute the given values
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[\square]{(-10)^2-4(1)(21)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[\square]{100-84}}{2} \\ \\ x=\frac{10\pm\sqrt[\square]{16}}{2} \\ \\ x=\frac{10\pm4}{2} \\ \\ x=7 \\ x=3 \end{gathered}[/tex]Find the value of y for x=7
y=x-3
y=7-3=4
the first solution is (7,4)
Find the value of y for x=3
y=3-3=0
the second solution is (3,0)
therefore
the answer is the first optionAB is a median of a triangle true or false
To answer this question, first we need to understand the definition of a median of a triangle.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex.
AB is a segment drawn from the vertex A, to the point B, but B is not the midpoint of the base of this triangle(the midpoint divides the segment into two equal parts, and since one part is 7 and the other is 8, B is not the midpoint
write the simplest polynomial equation with the given roots. -1, 2i please answer quickly
The polynomial equation with root of -1 and 2i is,
[tex]\begin{gathered} (x+1)(x+2i)(x-2i)=(x+1)(x^2-(2i)^2) \\ =(x+1)(x^2-4i^2) \\ =(x+1)(x^2+4) \\ =x^3+4x+x^2+4 \\ =x^3+x^2+4x+4 \end{gathered}[/tex]So simplest polynomial is,
[tex]x^3+x^2+4x+4[/tex]Out of 441 applicants for a job 235 have over five years of experience and 106 have over five years of experience and have a graduate degreeWhat is the probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience enter a fraction or round your answer to four decimal places if necessary
Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience = 106/441
Explanation:Total number of applicants, n(Total) = 441
Number of candidates that have over five years of experience, n(5 yrs) = 235
Probability that a randomly chosen applicant has over 5 years experience
[tex]\begin{gathered} P(5yrs)=\frac{n(5yrs)}{n(Total)} \\ \\ P(5yrs)=\frac{235}{441} \end{gathered}[/tex]Number of applicants that have over five years of experience and have a graduate degree, n(5 n g) = 106
Probability that a randomly selected applicant has over five years of experience and have a graduate degree
[tex]\begin{gathered} P(5\text{ n g\rparen = }\frac{n(5\text{ n g\rparen}}{n(Total)} \\ \\ P(5\text{ n g\rparen = }\frac{106}{441} \end{gathered}[/tex]Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience
[tex]\begin{gathered} P(g\text{ /5yrs\rparen = }\frac{P(5\text{ n g\rparen}}{P(5yrs)} \\ \\ P(g\text{ /5yrs\rparen = }\frac{106}{441}÷\frac{235}{441} \\ \\ P(g\text{ /5yrs\rparen=}\frac{106}{441} \end{gathered}[/tex]2. When is it important to use a strict inequality vs a non-strict inequality?
A strict inequality is one which involves the use of
[tex]>\text{, }<\text{ or }\ne[/tex]A non-strict inequality is one which involves the use of
[tex]\ge\text{ or }\leq[/tex]A strict inequality is used in a case when the two values being compared or related to one another cannot be equal to one another. That is, they are different.
A non-strict inequality is used in case when there is a possibility that the two values being compared can be equal to one another.
Joy took off from a stop light and increased her speed until she reaches the speed limit. She kept her speed steady until she saw a sign saying the speed limit has been increased. Select the graph that represents this situation.
We are presented with a group of graphs in which the x-axis represents time and the y-axis represents speed.
We are told that Joy started by accelerating when she took off, which means the graph should start with a line with positive slope.
She then maintained her speed, which means the slope of the line is 0, orin other words, the line is parallel to the time axis.
Finally, we are told that she saw a sign saying the speed limit had been increased, so she probably accelerated again, meaning the line should have a positive slope again.
Thus, the graph representing the situation is the third option.
A tee box is 48 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation 0 = -16t^2+ 32t +48 givesthe time t in seconds when a golf ball is at height 0 feet on the fairway.What is the height of the ball at 1 second and is the ball at its maximum height at 1 second (explain)?
Answer:
Step by step explanation:
what do you do when you solve for X.
Using the property vertically opposite angles and the corresponding angles, the value of x can be determine as,
[tex]\begin{gathered} 19x-4=110 \\ 19x=114 \\ x=6 \end{gathered}[/tex]Thus, the required value of x is 6.
Find the volume of the given prism. Round to the nearest tenth if necessary.A.2,511.5 yd^3B.1,255.7 yd^3C.1,025.3 yd^3D.1,450.0 yd^3
Given:
The sides of an equilateral triangle base are 10 yds. The height of the prism is 29 yds.
To find:
The volume of the prism.
Solution:
The formula of the volume of the triangular prism is given by:
[tex]V=\text{ (area of base)}\times\text{ (height of the prism)}[/tex]It is known that the area of the equilateral triangle is given by:
[tex]A=\frac{\sqrt[]{3}}{4}(side)^2[/tex]So, the area of the base of the triangular prism is:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(10)^2 \\ =\frac{1.732}{4}\times100 \\ =\frac{173.2}{4} \\ =43.30 \end{gathered}[/tex]Now, the volume of the given triangular prism is:
[tex]\begin{gathered} V=43.30\times29 \\ =1255.7\text{ yad\textasciicircum{}3} \end{gathered}[/tex]determine whether or not each spaceship trip below has the same speed as Saiges spaceship
1) Since Saige's spaceship makes 588 km in 60 seconds we can find its velocity:
[tex]\begin{gathered} V=\frac{d}{t} \\ V=\frac{588}{60}=\frac{49}{5}\text{ =9.8 km /s} \\ \\ V_2=\frac{441}{45}=\frac{49}{5} \\ V_3=\frac{215}{25}=\frac{43}{5} \\ V_4=\frac{649}{110}=\frac{59}{10} \end{gathered}[/tex]2) After simplifying we can state:
441/45 = has the same speed as Saige's spaceship
215/25 = does not have the same speed as Saige's space
649/110 =does not have the same speed as Saige's space