In this problem, we have a Binomial Probability Distribution
so
n=700
x=700*(8.9/100)=62.3=62
[tex]P(x=62)=\frac{700!}{62!(700-62)!}\cdot0.10^{(62)}\cdot0.90^{(700-62)}[/tex]P(x=62)=0.0313
the aprroximate probability is 3.13%Find MK. ML = 8, LK = x + 2, MK = 4x - 2
From the given description, it appears that M, L, and K are collinear and the length of MK is equal to the sum of ML and LK.
To be able to find the length of MK let's first find the value of x using the equation of the sum of the lines.
[tex]\text{ }\bar{\text{ML}}\text{ + }\bar{\text{LK}}\text{ = }\bar{\text{MK}}[/tex]Let's plug in the values given in the description.
[tex]\text{ (8) + (x + 2) = 4x - 2}[/tex][tex]\text{ 8 + x + 2 = 4x - 2}[/tex][tex]\text{ x + 10 = 4x - 2}[/tex][tex]\text{ x - 4x = -2 - 10}[/tex][tex]\text{ -3x = -12}[/tex][tex]\text{ }\frac{\text{-3x}}{-3}\text{ = }\frac{\text{-12}}{-3}[/tex][tex]\text{ x = 4}[/tex]Let's plug in x = 4 in the equation for the length of MK = 4x - 2.
[tex]\text{ }\bar{\text{MK}}\text{ = 4x - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 4(4) - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 16 - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 1}4[/tex]Therefore, the length of MK is 14.
round to the nearest ten-thousandth -7(10^x)=-54
The value x in the given expression is 0.8873.
Define logarithm.The power to which a number must be raised in order to get additional values is known as the logarithm. This is the simplest way to express really large numbers. The fact that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms is shown by a number of significant properties of a logarithm.
The other technique to write exponents in mathematics is using logarithms. The base-based logarithm of a number equals another number. The exact opposite function of exponentiation is carried out by a logarithm.
Given expression -
-7(10^x)=-54
We can also write it as
7(10^x) = 54
Using the concept of logarithm, apply the log on both sides
log(7*[tex]10^{x}[/tex]) = log 54
Applying the identity of logarithm,
log 7 + log [tex]10^{x}[/tex] = log 54
x log 10 = log 54 - log 7
x log 10 = 0.8873
As value of log 10 = 1,
x = 0.8873
Hence the value x in the given expression is 0.8873.
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the table shows the number of hours worked and the total amount that each of the four people earned one weekendwhose pay rate was the best whose pay rate was the worst Based on the chart.
pay rate = money earned/hours worked
Gary's pay rate: $37/4 = $9.25 per hour
Tara's pay rate: $54.9/6 = $9.15 per hour
Lamont's pay rate: $27.6/3 = $9.2 per hour
Darius' pay rate: $46.5/5 = $9.3 per hour
best pay rate: Darius
worst pay rate: Tara
A rocket is fired from the ground. Its height, in feet, is represented by the function h(t)=-16^2 +48t, where t(in seconds) represents the amount of time in the air since takeoff. When does the rocket land on the ground?A. 2 secondsB. 3.5 secondsC. 3 secondsd. 4.5 seconds
Given the height to be represented by the function
[tex]h(t)=16^{(2+48t)}[/tex]The function f(x)= 4x is one to one Find A and B
Given:
[tex]f(x)=4x[/tex]a)
[tex]\begin{gathered} x=4f^{-1}(x) \\ f^{-1}(x)=\frac{x}{4}\text{ , for all x} \end{gathered}[/tex]Option C is the final answer.
b)
[tex]\begin{gathered} f(f^{-1}(x))=f(\frac{x}{4}) \\ =4(\frac{x}{4}) \\ =x \end{gathered}[/tex][tex]\begin{gathered} f^{-1}(f(x))=f^{-1}(4x) \\ =\frac{4x}{4} \\ =x \end{gathered}[/tex][tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]The length of a rectangle is 97 m and the width is 14 m find the area give your answer without units
The area of the rectangle is 1358
Explanation:length of the rectangle = 97m
width of the rectangle = 14m
Area of a rectangle = length × width
[tex]\begin{gathered} \text{Area = 97m }\times\text{ 14m} \\ Area\text{ }of\text{ the rectangle = }1358m^2 \end{gathered}[/tex]The area of the rectangle is 1358 (without units)
f (t) = 44 – 5 g(t) = 2t - 1 Find (f - g)(t)
To solve the given problems, we have to subtract the functions.
[tex](f-g)(t)=4t-5-(2t-1)[/tex]Then, we simplify
[tex](f-g)(t)=4t-5-2t+1=2t-4[/tex]Hence, the resulting function is 2t-4.4 numbers that are divisible by both 2 and 9
A Number to be divisible by 2, the last digit must be even.
divisible by 9 = sum of the digits must be divisible by 9:
So, 4 numbers:
18,36,54,72
two angles of a triangle measure 59° and 63°. if the longest side measures 28 cm find the length of the shortest side. round answers to the nearest tenth
The two angles of triangle are : 59 and 63 degrees.
Length of the longest side of traingle is 28cm.
In a triangle,
the smallest side is always opposite to the smallest angle of the triangle,
and the largest side is always opposite to the largest angle
The sum of all the angles in atriangle is 180 degree
let the other angle is x so,
x+63+59=180
x=180-59-63
x=58
So, the longest side of traingle is in the opposite of angle 63
the smallest side of triangle is in opposite of angle 58
Apply the Sine rule to find the side of the traingle which has an opposite angle of 58.
Sine formula is expressed as:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}^{}=\frac{c}{\sin C}[/tex]Let a be the smallest side and b be the longest side of triangle so,
A=58, B=63, b=28cm
Substitute the values, and solve for a,
[tex]\begin{gathered} \frac{a}{\sin58^{\circ}}=\frac{28}{\sin63^{\circ}} \\ a=\frac{28\times\sin58^{\circ}}{\sin63^{\circ}} \\ a=\frac{28\times(0.84804809)}{0.89100652} \\ a=\frac{23.74534652}{0.89100652} \\ a=26.6500 \\ a=26.7\operatorname{cm} \end{gathered}[/tex]The shortest length is 26.7cm
[tex]y = 3(x + 3)(x + 1)[/tex]Intercept form find the vertex
Answer:
(-2, -3)
Explanation:
If we have an equation with the form:
f(x) = ax² + bx + c
The vertex of the parabola is the point (-b/2a, f(-b,2a)).
So, to find the vertex, we need to write the equation y = 3(x + 3)(x + 1) as:
[tex]\begin{gathered} y=3(x+3)(x+1) \\ y=3(x^2+3x+x+3) \\ y=3(x^2+4x+3) \\ y=3x^2+12x+9 \end{gathered}[/tex]Then, the value of a is 3 and the value of b is 12. It means that -b/2a is equal to:
[tex]-\frac{b}{2a}=-\frac{12}{2(3)}=-\frac{12}{6}=-2[/tex]And f(-b/2a) = f(-2) is equal to:
[tex]\begin{gathered} y=3x^2+12x+9 \\ f(-2)=3(-2)^2+12(-2)+9 \\ f(-2)=3(4)-24+9 \\ f(-2)=12-24+9 \\ f(-2)=-3 \end{gathered}[/tex]Therefore, the vertex is the point (-2, -3)
Solve the right triangle. Round decimal answers to the nearest tenth. find RSfind RTfind angle T
Δ RST shown in the picture is a right triangle, we know the measure of ∠R and ∠S, and the length of side ST.
To determine the length of the missing angle, you have to remember that the sum of the inner angles of a triangle add up to 180º
Then we can calculate the measure of ∠T as follows:
[tex]\begin{gathered} \angle R+\angle S+\angle T=180 \\ 57+90+\angle T=180 \\ 174+\angle T=180 \\ \angle T=180-174 \\ \angle T=33º \end{gathered}[/tex]The measure of the missing angle is ∠T=33º
To determine the lengths of the missing sides RS and RT, you have to use the trigonometric ratios of sine, cosine, and tangent. These ratios are defined as follows:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypothenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]"θ" represents the angle of interest.
Using ∠R as a point of reference, side ST is across this angle so it is the side of the triangle "opposite" to it.
Side RS is next to ∠R, so it is the side "adjacent" to it.
The trigonometric ratio that shows the relationship between the opposite and adjacent sides to an angle is the tangent. Using the definition of the tangent you can determine the length of RS as follows:
[tex]\tan R=\frac{RS}{ST}[/tex]-First, write the expression for RS, which means that you have to pass "ST" to the left side of the equal sign by applying the opposite operation to both sides of it.
[tex]\begin{gathered} ST\tan R=ST\cdot\frac{RS}{ST} \\ ST\tan R=RS \end{gathered}[/tex]-Replace the expression with the values of ∠R and ST:
[tex]\begin{gathered} 15\cdot tan57=RS \\ 23.09=RS \\ RS\approx23.1 \end{gathered}[/tex]Side RS measures 23.1
Side RT is the longest side of the triangle, and thus, its hypothenuse. To determine its length using ∠R and side ST, you have to apply the definition of the sine:
[tex]\sin R=\frac{ST}{RT}[/tex]-Pass the term RT to the other side of the equation to take the term out of the denominators place:
[tex]\begin{gathered} RT\cdot\sin R=RT\frac{ST}{RT} \\ RT\cdot\sin R=ST \end{gathered}[/tex]-Next, divide both sides by the sine of R to write the expression for RT
[tex]\begin{gathered} RT\cdot\frac{\sin R}{\sin R}=\frac{ST}{\sin R} \\ RT=\frac{ST}{\sin R} \end{gathered}[/tex]-Now replace the expression with the values of ∠R and ST to determine the length of RT
[tex]\begin{gathered} RT=\frac{15}{\sin 57} \\ RT=12.58 \\ RT\approx12.6 \end{gathered}[/tex]Side RT measures 12.6
An equilateral triangle and a square have equal perimeters. The side of the triangle measures 8cm. What is the area of the square, in square centimeters?
Answer
Area of the square = 36 square cm
Step-by-step explanation:
Given:
The perimeter of an equilateral triangle = the perimeter of a square
In an equilateral triangle, all sides are equal
Each side of the equilateral triangle = 8cm
Perimeter of the equilateral triangle = 3 * 8cm
Perimeter of the equilateral triangle = 24cm
Since, perimeter of square = perimeter of an equilateral triangle
Perimeter of a square = 24cm
We need to find each side of the square
Perimeter of a square = 4s
24 = 4s
Divide both side by 4
24/4 = 4s/4
s = 6cm
Since the length of each side of the square is 6cm
Therefore, area = l^2
Area = 6 * 6
Area of a square = 36 square cm
Determine whether each data set has a positive relationship, negative relationship or no relationship.
Two groups of numbers have a positive relationship, when we can identify a pattern where the two variables increase together, a negative relationship when the two variables decrease together and no relationship when we can't identify any pattern.
For the first graph we can identify that as the temperature grows, the number of chirps also grows, therefore they have a positive relationship.
For the second graph we can't clearly identify any relationship between the two variables, therefore it has no relationship.
use the information given to answer the question.consider the textbook and its mathematical label.part Awhich statement is true?the answer questions is in the image
Solution:
Given the textbook and its mathematics label as shown below:
From the above shape of the book and label, the textbook takes the shape of a rectangular prism, while its label is rectangular in shape.
Thus, the textbook is best represented by a rectangular prism, while the label is best represented by a rectangle.
The third option is the correct answer.
Can you please help and Copy the pictures and put the answers
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Explanation:We trace each point on the x-axis to the corresponding point on the y-axis to have the following
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Find the shape, or rate of change, from the following table?
ANSWER
C. -6
EXPLANATION
The rate of change is the change in the dependent variable when the independent variable changes 1 unit. In this case, all columns in the table have a change in the x variable of 1, so the difference between each column in the y-row is the rate of change,
[tex]m=-9-(-3)=-15-(-9)=-21-(-15)=-6[/tex]Hence, the rate of change is -6.
Yolanda is riding in a bike race that goes through a valley and a nearby mountain range,The table gives the altitude (in feet above sea level) for the five checkpoints in the race,Use the table to answer the questions,CheckpointAltitude(feet above sea level)12,2242- 13731,5714-305218(8) How much lower is Checkpoints than check out 2909 i lower
Step 1
Write the given checkpoint altitude
Checkpoint 1 = 2224
Checkpoint 2 = -137
Checkpoint 3 = 1571
Checkpoint 4 = -39
Checkpoint 5 = -218
Step 2:
a) How much lower is checkpoint 5 than checkpoint 2
You will subtract checkpoint 5 altitude from checkpoint 2
[tex]\begin{gathered} =\text{ -137 - (-218)} \\ =\text{ -137 + 218} \\ =\text{ 81 f}eet \end{gathered}[/tex]b) Altitude of the top hill that is 365 above checkpoint 5.
[tex]\begin{gathered} \text{Altitude of the top hill = 365 - 218 } \\ \text{Altitude of the top hill 365 above checkpoint 5 = 147} \end{gathered}[/tex]The area of the trapezoid is 14 square feet. Write an equation that you can use to find the value of x
Explanation
the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
[tex]A=(\frac{base1+base2}{2})\cdot\text{heigth}[/tex]then
Step 1
Let
base1=2x
base2=x
height= 2 ft
area= 14 square feet
replace,
[tex]\begin{gathered} A=(\frac{base1+base2}{2})\cdot\text{heigth} \\ 14=(\frac{2x+x}{2})\cdot\text{2 } \\ 14=(\frac{3x}{2})\cdot2 \\ 14=3x\rightarrow equation \\ divide\text{ both sides by 3} \\ \frac{14}{3}=\frac{3x}{3} \\ \frac{14}{3}=x \\ x=\frac{14}{3} \end{gathered}[/tex]then put 3x in the box.
I hope this helps you
2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.
Given:
The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.
Required:
To find the perimeters of the quadrilaterals.
Explanation:
The quadrilaterals are similar and the similarity coefficient is k = 1.25.
If the quadrilateral is similar then the ratio of their corresponding sides is equal.
Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x
Now
[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]Thus the perimeter of the one quadrilateral is 10dm.
The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm
Final Answer:
Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.
What is the volume of a cylinder whose base diameter is 10 cm and whose height is 12 cm? Round your answer to the nearest tenth.
Solution
We are given the following
Diameter = 10cm
Radius = 10/2 = 5cm
Height = 12cm
Therefore, the Volume will be
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=\pi(5^2)(12) \\ \\ Volume=\pi\times25\times12 \\ \\ Volume=300\pi \\ \\ Volume=942.5cm^3\text{ \lparen to the nearest tenth\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 942.5cm^3\text{ } \end{equation*}[/tex]A business person invests $3,367 at 5% compounded semiannually for two years. What is the future value of the investment, and how much interest will they earn over the two-year period?
The future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
Given that business person invests $3,367 at 5% compounded semiannually for two years.
p = $3,367
r = 5%
t = 2 years
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 3,367(1 + 5/100)²
A = 3,367(1 + 0.05)²
A = 4.700 (1.05)²
A = 3712.1175
Rounded to the nearest cent
A = $3712.1
Total interest = A - p = 3712.1 - 3,367 = $345.1
Therefore, the future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
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Which of the following describes the image of the transformation graphed to the right?A.) T(x,y)=(x+7,y-7)B.) T(x,y)=(x-7,y-7)C.) T(x,y)=(x+7,y+7)D.) T(x,y)=(x-7,y+7)
Answer:
D.) T(x,y)=(x-7,y+7)
Step-by-step explanation:
Function f(x,y).
Transformation along the x axis:
Moving a units to the left: We have f(x+a,y).
Moving a units to the right: We have f(x - a,y).
Transformation along the y axis:
Moving a units up: We have f(x, y-a).
Moving a units down: We have f(x, y+a).
In this question:
The function is moved 7 units to the right among the x-axis(x - 7) and 7 units down along the y axis(y + 7).
So the answer to this question is:
D.) T(x,y)=(x-7,y+7)
5x+10=-25solving for x
start by substracting 10 on both sides
[tex]\begin{gathered} 5x+10-10=-25-10 \\ 5x=-35 \end{gathered}[/tex]divide by 5 on both sides
[tex]\frac{5x}{5}=-\frac{35}{5}[/tex][tex]x=-7[/tex]: + = 27 = + 3. (15,12). (12,15). (6,21).
(12, 15) (option B)
Explanation:x + y = 27 ..equation 1
y = x + 3 ...equation 2
Using substitution method:
We would substitute for y = x + 3 in equation 1
x + (x + 3) = 27
x + x + 3 = 27
2x + 3 = 27
2x = 27 - 3
2x = 24
x = 24/2
x = 12
Substitute 12 for x in equation 2:
y = 12 + 3
y = 15
The solution to both equations (x, y):
(12, 15) (option B)
Suppose there is a simple index of three stocks, stock X, stock Y, and stock Z. Stock X opens the day with 5000 shares at $4.10 per share. Stock Y opens the day with 2000 shares at $4.50 per share. Stock Z opens the day with 4000 shares at $3.60 per share. The simple index rises 3.4% over the course of the day. What is the value of the index at the end of the day? Round your answer the nearest hundred. A. $45,100 B. $43,900 C. $45,400 D. $44,800
Solution:
Step 1:
Calculate the total value of stock X
[tex]\begin{gathered} =5000\times\text{ \$}4.10 \\ =\text{ \$}20,500 \end{gathered}[/tex]Step 2:
Calculate the total value for Stock Y
[tex]\begin{gathered} =2000\times4.5 \\ =\text{ \$}9000 \end{gathered}[/tex]Step 3:
Calculate the total value for stock Z
[tex]\begin{gathered} =4000\times\text{ \$}3.60 \\ =\text{ \$}14,400 \end{gathered}[/tex]Step 4:
Calculate the total value of the shares but without the increase yet
[tex]\begin{gathered} 20,500+9000+14,400 \\ =\text{ \$}43,900 \end{gathered}[/tex]Step 5:
Calculate the increase in the simple index
[tex]\begin{gathered} =\frac{3.4}{100}\times43900 \\ =\text{ \$}1,492.60 \end{gathered}[/tex]Step 6:
Add the increase in the simple index to the total value of the shares
[tex]\begin{gathered} 43,900+1,492.60 \\ =\text{ \$}45,392.60 \\ \approx\text{ \$}45,400 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\text{\$}45,400[/tex]OPTION C is the right answer
Answer:
45,400
Step-by-step explanation:
just took test AP3
using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 4 years Original cost = 13,850 The current market value is $ _
The current market value is $9086.98
In this problem, supposing a decay of 10% a year, and the original value of $13,850, the parameters are A(0) = 13850, r = 0.1.
Using exponential decay formula, the value of the car in 4 years is given by:
A(t) = A(0)(1 - r)^t
A(4) = 13850(1 - 0.1)^4
A(4) = 13850 * (0.9)^4
A(4) = 9086.98
Therefore, The current market value is $9086.98
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It’s given that the shape is not a parallelogram but why?
They are two congruent triangles.
Given the expression: 6x^10 - 96x^2Part A: Rewrite the expression by factoring out the greatest common factor.Part B: Factor the entire expression completely. Show the steps of your work.
According to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
The given expression is -
[tex]6x^{10}-96x^{2}[/tex] ---- (1)
We have to -
A: Rewrite the expression by factoring out the greatest common factor.
B: Rewrite the expression by factoring the entire expression completely.
Solving for Part A:
From equation (1), we have
[tex]6x^{10}-96x^{2}[/tex]
Applying the distributive property, we can rewrite this as -
[tex]6x^{10}-96x^{2}\\=6x^{2} x^{8}-6x^{2}*16\\=6x^{2}(x^{8}-16)[/tex]------- (2)
This is the expression obtained by factoring out the greatest common factor that is [tex]x^{2}[/tex].
Solving for Part B:
From equation (2), we have
[tex]6x^{2}(x^{8}-16)[/tex]
Applying the difference of squares concept, we can rewrite this as -
[tex]6x^{2}(x^{8}-16)\\=6x^{2}[(x^{4} )^{2} -4^{2} ]\\=6x^{2}(x^{4}+4)(x^{4}-4)\\=6x^{2}(x^{4}+4)[(x^{2} )^{2}-2^{2} ]\\=6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex]
This is the expression obtained by factoring the expression completely.
Therefore, according to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
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Assume that a varies directly as b.When the value of a is 5,the value of b is 18.When the value of a is 22,what is the value of b?
In this case we have the proportion 18:5, then we have the equation
[tex]\begin{gathered} \frac{18}{5}=\frac{b}{22} \\ b=\frac{18}{5}\times22 \\ b=\frac{396}{5} \end{gathered}[/tex]Then, when a is 22, the value of b is 396/5 that is also equal to 79.2 or
[tex]79\frac{1}{5}[/tex]For a field trip 22 students rode in cars and the rest filled 5 buses how many students were in each bus if 317 students were on the trip.
We have to find how many students were in each bus.
We can call this quantity "x".
The total number of students is 317.
This quantity can be divided in the number of students that rode in cars, 22, and the rest went in 5 buses.
The quantity that rode in bus can be expressed as 5x.
Then we can write:
[tex]22+5x=317[/tex]We can solve this as:
[tex]\begin{gathered} 22+5x=317 \\ 5x=317-22 \\ 5x=295 \\ x=\frac{295}{5} \\ x=59 \end{gathered}[/tex]Answer: there were 59 students in each bus.