Let's go over each of the expressions and see if they are equal to 1/8
[tex]2^{-3}=\frac{1}{2^3}=\frac{1}{8}[/tex]So A is equivalent
[tex](-8)^1=-8[/tex]So B is not equivalent
[tex](\frac{32}{4})^{-1}=\frac{1}{\frac{32}{4}}=\frac{4}{32}=\frac{1}{8}[/tex]So C is equivalent
[tex]8^8-8^9=-117440512[/tex]So D is not equivalent
[tex]\frac{8^8}{8^9}=8^{8-9}=8^{-1}=\frac{1}{8}[/tex]So E is equivalent
[tex]undefined[/tex]An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are B = 8°and 8 = 12.5 (see figure). How far apart are the ships? (Round your answer to one decimal place.)
ANSWER:
911.6 ft
EXPLANATION:
Given:
[tex]\begin{gathered} \theta=12.5^{\circ} \\ \beta=8^{\circ} \end{gathered}[/tex]To find:
The distance between the two ships
Let's go ahead and draw a sketch as seen below;
Let's go ahead and solve for the value of AC by taking the tangent of angle 12.5 degrees as seen below;
[tex]\begin{gathered} \tan12.5=\frac{350}{AC} \\ \\ AC=\frac{350}{\tan12.5} \\ \\ AC=1578.7\text{ }ft \end{gathered}[/tex]Let's now solve for the value of AD by taking the tangent of angle 8 degrees as seen below;
[tex]\begin{gathered} \tan8=\frac{350}{AD} \\ \\ AD=\frac{350}{\tan8} \\ \\ AD=2490.4\text{ }ft \end{gathered}[/tex]Therefore the distance between the two ships will be;
[tex]\begin{gathered} CD=AD-AC \\ CD=2490.4-1578.7 \\ CD=911.6\text{ }ft \end{gathered}[/tex]So the two ships are 911.6 ft
I need help in this , please help me !!!!!!
EXPLANATION
The coordinate son the plane when x=-3 are y=9 ---> A= (-3,9)
The points on the parabola when y= 16 are x=4 ---> (x_1,y_1) = (4,16) and (x_2,y_2) = (-4,16)
60x+110y= 265 120x+90y=270
EXPLANATION
Given the system of equations:
(1) 60x + 110y = 265
(2) 120x + 90y = 270
We can apply the substraction method as shown as follows:
Multiply 60x + 110y = 265 by 2:
----> (60x + 110y = 265)*2 -------> 120x + 220y = 530
Subtract the equations:
120x + 220y = 530
- (120x + 90y = 270)
--------------------------------
130y = 260
Divide both sides by 130:
y= 260/130
Simplifying:
y= 2
Replacing on the first equation:
60x + 110(2) = 265
Applying the distributive property:
60x + 220 = 265
Subtracting 220 to both sides:
60x = 265 - 220
Subtracting like terms:
60x = 45
Dividing both sides by 60:
x = 45/60
Simplifying:
x= 3/4
The solutions to the system of equations are:
x=3/4 y=2
0.6 divided by 30 I don’t know how to divide decimals to well
Given: 0.6 divided by 30
We will find the result as follows:
[tex]0.6\div30=\frac{6}{10}\times\frac{1}{30}=\frac{6}{300}=\frac{1}{100}\times\frac{6}{3}=\frac{2}{100}=0.02[/tex]So, the answer will be 0.02
A teacher showed this animal to students on a field trip. Which tool will allow the students to best see the animal up close? O A Tape measure O B Graduated cylinder O c. Notebook O D. Hand lens Submit
ANSWER is hands lens.
This is the best tool to see the animal up close.
A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results: Even number = lose $51 or 3 = win $15 = win $8What is the expected value of the game?State your answer in terms of dollars rounded to the nearest cent (hundredth).
To answer this question, we need to find, first of all, the corresponding probability for the events. Then, we have:
1. The probability of an even number is:
We have that in a single 6-sided die, we have that the only even numbers are 2, 4, and 6. If we roll the die one time, then the probability of this event is:
[tex]P(\text{even)}=\frac{3}{6}[/tex]2. The probability of resulting 1 or 3 is - if the die is rolled one time:
[tex]P(1,3)=\frac{2}{6}[/tex]3. The probability of resulting in a 5 is - if the die is rolled one time:
[tex]P(5)=\frac{1}{6}[/tex]Then, if we add all the corresponding probabilities we have:
[tex]P(\text{total)}=\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\frac{6}{6}=1[/tex]The expected value of the gameTo find the expected value of the game, we have to find the product of the probability by the corresponding amount of money of the event as follows:
[tex]E(v)=\frac{3}{6}\cdot-\$5+\frac{2}{6}\cdot\$1+\frac{1}{6}\cdot\$8[/tex][tex]E(v)=-\$2.5+\$(\frac{1}{3})+\$(\frac{4}{3})=-\$2.5+\$(\frac{5}{3})=-\$(\frac{5}{6})=-\$0.833333333333[/tex]Or
[tex]E(v)=-\$0.833333333333[/tex]If we round the answer in terms of dollars rounded to the nearest cent (hundredth), we have that the expected value is:
[tex]E(v)=-\$0.83[/tex]In other words, if we play the game, we will expect to lose 83 cents of a dollar (per game) or 0.83 dollars.
In summary, we have that the expected value of the game is -$0.83.
what is LK rounded to the nearest hundredth?what is JK rounded to the nearest hundredth?
LK = 2.91m
JK = 7.99m
Explanation:hypotenuse = 8.5m
angle = 20°
LK = side opposite the angle 20°
Since we know the hypotenuse and we need to find the opposite, we would apply sine ratio
sine ratio = opposite/hypotenuse
sin 20° = LK/8.5
LK = 8.5(sin 20°)
LK = 8.5(0.3420)
LK = 2.907
To the nearest hundredth, LK = 2.91m
JK = base = adjacent
We would apply cosine ratio
cos 20° = adjacent/hypotenuse
cos 20° = JK/8.5
JK = 8.5(cos20°)
JK = 8.5(0.9397)
JK = 7.98745
To the nearest hundredth, JK = 7.99m
Find the Vale of X, round your awsner to the nearthest tenth
The required value of the x is given as 8.66 for the given triangle.
Given that,
A figure of the triangle is shown, with the help of trigonometric operators we have to determine x.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
Tan60 = x/ 5
x = tan60 × 5
x = 1.732 × 5
x = 8.66
Thus, the required value of the x is given as 8.66 for the given triangle.
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please please pleaseee help mee i have to finish my credit by may 20th
Answer:
[tex]C[/tex]Explanation:
Using the graph of both equations, we want to get the correct option
We start by making a plot of the two on same axes
We have the plot of the functions as follows:
Now, let us take a look at the options:
a) This is wrong. The functions have two intersection points
b) This is incorrect. They have equal y-intercepts at y = 2
c) This is correct. The quadratic function have a greater maximum
2. Find the difference of 6x - 3x^2 and - 5x^2 - 6x +1. Write your final solution in standard form!
To start, we need write the polynomials:
[tex]6x-3x^2and-5x^2-6x+1[/tex]Now we gonna find the difference between first polynomial and second, like this:
tip: Special care with operate signs.
[tex]\begin{gathered} 6x-3x^2-(-5x^2-6x+1);\text{ we operate with signs over here}\ldots \\ 6x-3x^2+5x^2+6x-1;\text{ We }put\text{ together terms with similar exponent in parentheses, like this:} \\ (5x^2-3x^2)+(6x+6x)-1;\text{ we operate}\ldots \\ 2x^2+12x-1. \end{gathered}[/tex]That is the final solution, you can solve that polynomial if you need.
[tex]2x^2+12x-1.[/tex]Find the sum: 73 + 751 + 1,239 + 13,907 =
Answer:15,970
Step-by-step explanation:
Part A. 2.7 is 60% of what number?Part B. 4.2 is 10% of what number ?Part C. 214.6 is what percent of 58 ?
Part A)
2.7 --- 60%
Therefore in order to know what is the 100% we will do the next operation
[tex]\frac{1\times2.7}{0.6}=4.5[/tex]2.7 is 60% of 4.5
Part B)
4.2 --- 10%
In order to know the 100% we will do the next operation
[tex]\frac{1\times4.2}{0.10}=42[/tex]4.2 is 10% of 42
Part C)
58 --- 100%
214.6 --- ?
[tex]\frac{214.6\times1}{58}=3.7=370\text{\%}[/tex]214.6 is 370% of 58
If a seed is planted, it has a 85% chance of growing into a healthy plant 9 seeds are planted, what is the probability that exactly 3 don't grow?
ANSWER
0.1069
EXPLANATION
We have two possible outcomes for each experiment: the seed grows or the seed does not grow. So, this follows a binomial distribution, where, in this case, the probability of success is the probability that a seed does not grow - note that we want to find what is the probability that a number of seeds do not grow.
We know that the probability that a seed grows is 85%, so there is a 15% chance the seed does not grow. This experiment is repeated 9 times (9 seeds) and we want to find what is the probability that the number of successes is 3 - remember that "success" is that the seed doesn't grow.
To find this, we have to use the binomial probability formula,
[tex]P(X=x)=\binom{n}{x}\cdot p^x\cdot q^{n-x}[/tex]For this problem:
• n = 9
,• x = 3
,• p = 0.15
,• q = 0.85
So we have,
[tex]P(X=3)=\binom{9}{3}\cdot0.15^3\cdot0.85^6\approx0.1069[/tex]Hence, the probability that exactly 3 seeds don't grow is 0.1069, rounded to four decimal places.
7x - 2x + 4 = 8 - 3x what's the value of x
The initial equation is:
[tex]7x-2x+4=8-3x[/tex]so we can move all term with x to the left and the constants to the right so:
[tex]\begin{gathered} 7x-2x+3x=8-4 \\ 8x=4 \end{gathered}[/tex]Now we divide by 8 bout side of the equation so:
[tex]\begin{gathered} x=\frac{4}{8} \\ x=\frac{1}{2} \end{gathered}[/tex]Given a family with four children, find the probability of the event. The youngest is a boy, given that the birth order alternates between girls and boys is
Given that the birth alternates between a boy and a girl, there are 2 options which are as follows.
Let
G = Girls
B = boys
Therefore,
[tex]\begin{gathered} \text{GBGB} \\ BGBG \end{gathered}[/tex]The probability that the youngest will be a boy in this scenario will be
[tex]\frac{1}{2}[/tex]Fill in the table using this function rule.y= 4x-3
the initial function is:
[tex]y=4x-3[/tex]now we replace the values in x that gives the table so:
for -2:
[tex]\begin{gathered} y=4(-2)-3 \\ y=-8-3 \\ y=-11 \end{gathered}[/tex]for 0:
[tex]\begin{gathered} y=4(0)-3 \\ y=-3 \end{gathered}[/tex]for 2:
[tex]\begin{gathered} y=4(2)-3 \\ y=5 \end{gathered}[/tex]for 4:
[tex]\begin{gathered} y=4(4)-3 \\ y=13 \end{gathered}[/tex]What is the rule of the pattern below? 52, 48, 44, 40, 36....
Answer:
Subtract 4
Explanation:
In the number pattern:
[tex]52,48,44,40,36...[/tex]We subtract the next term from the previous term below:
[tex]\begin{gathered} 48-52=-4 \\ 44-48=-4 \\ 40-44=-4 \end{gathered}[/tex]We see that each one gives a subtraction of 4.
Therefore, the rule of the pattern is 'Subtract 4'.
C is the depth in meters and f(x) is in grams of salt kilograms of sea water approximate the salinity to the nearest hundredth) when the depth is 797 meters
Using the function f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg
How to find the salinity at the required depthThe salinity s calculated using the logarithmic function model
f(x) = 28.7 + 1.2log (x + 1)
given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters
for x = 797 meters
f(x) = 28.7 + 1.2log (x + 1)
f(x) = 28.7 + 1.2log (797 + 1)
f(x) = 28.7 + 1.2log (798)
f(x) = 28.7 + 1.2 * 2.902
f(x) = 28.7 + 3.4824
f(x) = 32.1824
f(x) = 32.18 (to the nearest hundredth)
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The members of an adult soccer team are planning a party for their children. The histogram below shows the number of children each team member will bring to the party, (*If you can't see the histogram below, click on the attached pdf to view.) Members of soccer team Frequency 1 2 Number of children attending party
6The mean number of children each team member will bring
Here, we want to get the mean number of students that each team member willl bring
From the histogram, we can deduce the following;
a) 4 team members will bring no (0) children
b) 3 team members will bring 1 children each
c) 5 team members will bring 2 children each
d) 2 team members will bring 3 children each
e) 1 team member will bring 5 children
So the totla number of children at the party will be;
4(0) + 3(1) + 5(2) + 2(3) + 1(5)
= 0 + 3 + 10 + 6 + 5 = 24 children
The number of team members is 4 + 3 + 5+2 + 1 = 15
So, the mean number each will bring is; the number of children attending the party divided by the number of team members
[tex]\frac{24}{15}\text{ = 1.6}[/tex]What's the inverse operation of a cubing number?Also, can you please solve and explain this examples?
The inverse of cubing a number is applying cubic root
[tex]a^3\leftrightarrow\sqrt[3]{a}[/tex]Now, let's go through the examples:
When you want to find the square root of a number x you have to ask yourself:
Which number, when multiplied by itself, will give me x ?
For example,
[tex]\sqrt[]{225}=15[/tex]Because
[tex]\begin{gathered} 15\times15=225 \\ 15^2=225 \end{gathered}[/tex]This way,
[tex]\begin{gathered} \sqrt[]{49}=7\Leftrightarrow7^2=49 \\ \sqrt[]{121}=11\Leftrightarrow11^2=121 \\ \sqrt[]{1600}=40\Leftrightarrow40^2=1600 \end{gathered}[/tex]Now for the cubic root:
When you want to find the cubic root of a number y you have to ask yourself:
Which number, when multiplied by itself two times, will give me y ?
For instance,
[tex]\sqrt[3]{64}=8[/tex]Because
[tex]\begin{gathered} 8\times8\times8=64 \\ 8^3=64 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sqrt[3]{8}=2\Leftrightarrow2^3=8 \\ \sqrt[3]{1}=1\Leftrightarrow1^3=1 \\ \sqrt[3]{2744}=14\Leftrightarrow14^3=2744 \end{gathered}[/tex]which statement is true about the cost of a frozen dessert?
The cost function is,
[tex]c=0.35y+1.25[/tex]The cost of 15 ounce container is,
[tex]\begin{gathered} c=0.35\times15+1.25 \\ c=6.5 \end{gathered}[/tex]Thus, option (A) is the correct solution.
How do you answer these questions? How do you know whether a given value is a solution to the inequality?
We have the following inequality:
x > - 0.75
This is the same as state "x is greater than -0.75". Therefore, any value greater than -0.75 is a solution to this inequality
Considering this rule, we can answer each item:
a) The statement "-0.75 is a solution to the inequality" is FALSE, because, or rule states that x must be greater than -0.75.
b) The statement "There are many solutions to this inequality" is TRUE. Actually, there is an infinite number of solutions to this inequality (some of them can be expressed by -0.74, -0.73, -0.72...)
c) The statement "All the solutions to the inequality are negative" is FALSE, since any positive (or null) number is also greater than -0.75.
d) The statement "The inequality -0.75 < x is equivalent to the given inequality" is TRUE, since this inequality is tha same as the statement "-0.75 is less than x", which is a different form of express the original statement "x is greater than -0.75".
e) The statement "-4.5 is a solution to the inequality" is FALSE, because -4.5 is less than -0.75, which contradicts or rule.
an octagon has side lengths 10.9 in the perimeter of the Octagon is 87.2 in centimeter and the area is 573.67 inches squared a second octagon has corresponding side lengths equal to 18.03 in find the area of the second octagon round to the nearest tenth
The are of the octsagon is given by:
[tex]A=2a^2(1+\sqrt[]{2})[/tex]where a is the lenght of its side.
Since the second octagon has sile lengths equal to 18.03, its area is:
[tex]A=2(18.03)^2(1+\sqrt[]{2})=1563.6[/tex]Therefore the area is 1563.6 squared centimeters
which is an equation
The slope is define as the rate of y coordinate with respect to the x coordinate.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]In the line D which is parallel to x axis has the constant y coordinate i.e
y = -3
So, for the numerator of the slop for line D is ( -3) - ( -3) = 0
Thus the slope will be express as :
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{-3-(-3)}{x_2-x_1} \\ \text{Slope}=\frac{0}{x_2-x_1} \\ \text{Slope = }0 \end{gathered}[/tex]Thus the slope of line is 0
Now, for the line A :
The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.
i.e. x = -5
So, substitute the value in the expression for the slope :
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{y_2-y_1}{-5-(-5)_{}} \\ \text{Slope}=\frac{y_2-y_1}{-5+5_{}} \\ \text{Slope = }\frac{y_2-y_1}{0_{}} \\ If\text{ the denominater becomes zero, then the expression is not define} \\ So,\text{ slope of line A is not define} \end{gathered}[/tex]Slope of line A is not define
In the line B and C, the coordinates of x and y aixs are changes countinously
thus thier slopes will be well define.
Answer : Slope of line A is not define.
what is the average rate of change f (t) t=0 t=236 seconds per second -36 feet per second -18 seconds per second 18 feet per second
A high school teacher grades a math test. She wants to see the numericalgrade of each student. Which item should she use so she can quickly seehow many students got each score? A. Line plot B. None of these C. Frequency table D. Pie chart
Given: A high school teacher grades a math test. She wants to see the numerical grade of each student.
Required: To identify which item the teacher should use so she can quickly see
how many students got each score.
Explanation: A line plot is a plot that shows the frequency of data along a number line as shown in the figure below-
If you place these marbles in a bag,close your eyes, and choose a marble,what is the probability that it will beblue?Simplify the fraction.Enter the number that belongs in the green box.
The following information below can be obtained from the image;
Blue Marbles: 6
Red Marbles: 5
Yellow Marbles: 3
Total marbles = 14
The probability of an event, E, is given as:
[tex]\begin{gathered} Pr(E)\text{ = }\frac{number\text{ of favourable outomes}}{number\text{ of sample space}} \\ \text{Thus, the probability of of choosing a blue marble is;} \\ Pr(\text{choosing a blue marble)=}\frac{number\text{ of blue marbles}}{number\text{ of total marbles}} \\ Pr(choo\sin g\text{ a blue marble) = }\frac{6}{14} \\ \text{In simplified form;} \\ Pr(\text{choosing a blue marble)=}\frac{3}{7} \end{gathered}[/tex]Hence, the number that belongs in the green box is 3
Michiko has one quiz each week in social studies class. The table gives the probability of having a quiz on eachday of the week. What is the probability that Michiko will not have a quiz on Wednesday? Express your answeras a percent.
Solution:
Given:
From the table, the probability that Michiko will hava a quiz on Wednesday is 0.070.
This is the probability of success.
Hence, the probability that Michiko will not have a quiz on Wednesday is the probability of failure.
Thus,
[tex]\begin{gathered} p+q=1 \\ \text{where;} \\ p\text{ is the probability of success} \\ q\text{ is the probability of failure} \\ \\ p=0.070 \\ q=\text{?} \end{gathered}[/tex][tex]\begin{gathered} p+q=1 \\ q=1-p \\ q=1-0.070 \\ q=0.93 \end{gathered}[/tex]Hence, the probability of failure (the probability that Michiko will not have a quiz on Wednesday is 0.93.
As a percent,
[tex]\begin{gathered} q=0.93\times100 \\ q=93\text{ \%} \end{gathered}[/tex]Therefore, the probability that Michiko will not have a quiz on Wednesday is 93%
A regular pentagon is shown below. Supposethat the pentagon is rotatedcounterclockwise about its center so that thevertex at E is moved to C, how many degreesdoes that pentagon rotate?
Solution:
Given:
A regular pentagon rotated counterclockwise about its center.
To get the angle by which it rotated, we draw lines from each of the vertexes to the center to divide the pentagon into 5 equal triangles as shown;
The angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;
[tex]\angle EOC[/tex]To get angle EOC, we use the property of the sum of angles at a point.
The sum of angles at a point is 360 degrees.
[tex]\angle AOB+\angle BOC+\angle COD+\angle DOE+\angle EOA=360^0[/tex]
Since it is a regular polygon, each of these angles is equal.
Hence,
[tex]\begin{gathered} \angle AOB=\angle BOC=\angle COD=\angle DOE=\angle EOA=x \\ \angle AOB+\angle BOC+\angle COD+\angle DOE+\angle EOA=360^0 \\ x+x+x+x+x=360^0 \\ 5x=360^0 \\ \text{Dividing both sides by 5;} \\ x=\frac{360}{5} \\ x=72^0 \end{gathered}[/tex]
Thus, the measure of angle EOC is;
[tex]\begin{gathered} \angle EOC=\angle COD+\angle DOE^{} \\ \angle EOC=x+x \\ \angle EOC=72+72 \\ \angle EOC=144^0 \end{gathered}[/tex]Therefore, the angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;
[tex]\angle EOC=144^0[/tex]
What is the equation of the line perpendicular to 3x+y=-8 that passes through (-3,1)?
Before we calculate the perpendicular line, let's rewrite our line equation in slope-intercept form. The slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Rewritting our equation, we have
[tex]\begin{gathered} 3x+y=-8 \\ y=-3x-8 \end{gathered}[/tex]This means the slope of our line is equal to - 3.
Two perpendicular lines are related by their slope. Let's say two lines are perpendicular, this means the slope of one of the lines is equal to minus the inverse the slope of the other. If we call the slope of one of those lines as m_1, the slope of the perpendicular line m_2 is given by
[tex]m_1=-\frac{1}{m_2}[/tex]Using this relation, we can find the slope of a perpendicular line. Since the slope of our line is equal to - 3, then, the slope of the perpendicular line is
[tex]m_{\perp}=-\frac{1}{(-3)}=\frac{1}{3}[/tex]In slope-intercept form, our perpendicular line has the following form
[tex]y=\frac{1}{3}x+b[/tex]To find our y-intercept, we can use our given point that belongs to this line.
The point is (-3, 1), evaluating this point in our equation, we have
[tex]\begin{gathered} (1)=\frac{1}{3}\cdot(-3)+b \\ \Rightarrow1=-1+b \\ \Rightarrow b=2 \end{gathered}[/tex]Then, our line is
[tex]y=\frac{1}{3}x+2[/tex]