Answer:
15 feet
Step-by-step explanation:
Given an 8' object casts a 10' shadow, you want to know the length of the shadow of a 12' object.
ProportionThe shadow length is proportional to the object length:
shadow/object = 10'/8' = s/12'
Multiplying by 12', we have ...
s = (12')(10/8) = 15'
The shadow of a tree 12 feet tall will be 15 feet long.
Write the standard form of the equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5
The equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5 in standard form is 5y + 2x = -5
How to find the equation of a line?The equation of a line can be represented in standard form or slope intercept form as follows;
Slope intercept form,
y = mx + b
where
m = slopeb = y-interceptLine are parallel when they have the same slope.
Therefore, the slope of the equation has a slope of - 2 / 5 x.
The line passes through (-5, 1).
Hence, let's find y-intercept.
y = - 2 / 5 x + b
1 = - 2 / 5 (-5) + b
1 - 2 = b
b = -1
Therefore, y = -2 / 5x - 1.
The equation in standard form should be in the form Ax + By = C.
Hence,
y + 2 / 5 x = -1
5y + 2x = -5
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which is a reasonable estimate for the amount of kernels serena needs to make 6 cups of popcorn
Answer:
four tablespoons to make 6 cups of popcorn.
Step-by-step explanation:
1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.
tan 30 x cos 30 in exact value
(jk−1)÷j when j=−4 and k=−0.9
The evaluation of the expression for the given values of j and k is -0.65
Evaluating an ExpressionFrom the question, we are to evaluate the given expression for the given values of j and k.
From the given information,
The given expression is
(jk - 1) ÷ j
and
j = -4 and k = -0.9
Now, substitute the values of j and k into the expression
(jk - 1) ÷ j
((-4)(-0.9) - 1) ÷ -4
= (3.6 - 1) ÷ -4
= 2.6 ÷ -4
= - 0.65
Hence, the value of the expression is -0.65
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Ahlee i riding her bike to the beach. If the beach i 17 mile from her home, and he ha already travelled 3/5 of the way, how much farther doe he have to cycle?
The distance yet to be covered by Ashlee is 6.8 miles.
Ashlee is riding her bike to the beach. The beach is 17 miles from her home. She has already travelled 3/5 of the total distance. We need to find out how much farther she has to cycle.
Let the distance left to be covered by Ashlee be represented by the variable "D". The distance already covered by Ashlee on her cycle is calculated below.
d = (3/5)×17
d = 10.2
So she has already covered a distance of 10.2 miles. The distance yet to be covered is the difference between the total distance and the distance covered.
D = 17 - 10.2
D = 6.8
Hence, the distance yet to be covered by Ashlee is 6.8 miles.
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elect the correct answer. A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
The expected value of a player's winnings on each roll is: $30.
How can we calculate the expected value of a player's winnings on each roll?We can calculate the expected value of a player's value on each winning by first understanding that there are only two multiples of three on the six-sided die. These multiples are 3 and 6.
So, if 3 is obtained facing upward, the player wins 3 × 20 = $60
Also, if the player obtained 6 facing upward, the player wins 6 × 20 = $120
So, the total amount is $180.
However, the question expects us to calculate the expected value of a player's winnings on each roll. Thus, we will have $180 ÷ 6 = $30.
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A number cube with six sides numbered 1 through 6 is rolled. the probability of rolling a 5 is 16. what is the probability of not rolling a 5?
The probability of not rolling a 5 is [tex]\frac{1}{6}[/tex]
For any event A, the probability of not getting A is given by
[tex]P(not A)= 1- P(A)[/tex]
A number cube with six sides numbered 1 through 6 is rolled.
Then we have,
The total number of possible outcomes [tex]= 6[/tex]
Also, it is given that, The probability of rolling a 5 is
P(rolling 5)=[tex]\frac{1}{6}[/tex].
Now, the probability of not rolling a 5 will be
[tex]P(\text{not rolling a 5})= 1- P(\text{rolling 5})[/tex]
[tex]=1-\frac{1}{6}[/tex]
[tex]=\frac{5}{6}[/tex]
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1. Calculate arithmetic mean from the following data. 50, 60, 70, 80, 65, 70, 90
Answer:
Here ,
sigma x=50+60+65+70+70+80+90=485
N=7
now,
Mean =sigma x÷N
=485÷7
=69.28
How long would the minute hand of a clock have to be if its end were to move at 100km/hour?
To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers
What is angular velocity?Angular velocity is the rate and direction of rotation of a body about an axis.
The required linear speed of the minute hand = 100 km/hour
The formula to convert angular speed to linear speed is presented as follows;
[tex]\omega = \dfrac{v}{r}[/tex]Which gives;
[tex]r = \dfrac{v}{\omega}[/tex]The angular speed of the minute hand = 2·π rad/hour
The required length of the minute hand is therefore;
[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]
The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km
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Rupert has a bag containing 2 green, 3 purple and 2 orange marbles. He selects two marbles from
his bag in succession, without replacement.
Using a tree diagram, determine the probability that Rupert picked the two green marbles.
The probability that Rupert picked 2 green balls is 1/21.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.
Main Body:
total balls = 7 , green balls =2
1st try:
probability of getting green ball = 2/7
As there is no replacement so now,
total balls = 6 , green balls = 1
2nd try:
probability of getting green ball = 1/6
total probability = (2/7)*(1/6)
= 1/21
Hence the answer is 1/21.
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a simple random sample of 25 observations is dervied from a normally distributed population with a population standard deviation of 8.2. compute the margin of error with 80% confidence.
The margin of error with 80% confidence interval is 2.099
Given that,
A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.
To find : The margin of error with 80% confidence
Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
Here we have
n=25,σ=8.2
For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is
ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992
Thus, with 80% confidence, the error margin is 2.099.
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a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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a coin is altered so that the probability that it lands on heads is less than 1 2 12 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1 6 16. what is the probability that the coin lands on heads?
The probability that the coin lands on heads is D = (3±√3)/6
Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.
Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.
The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities
(4+2)x2(1-x)2 = 1/6
6x2(1-x)2 = 1/6
x2(1-x)2 = 1/36
x(1-x) = ±1/6
As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence
x(1-x) = 1/6
6x2 – 6x +1 = 1/6
Using the quadratic formula, we can determine that the roots of this equation are
(3±√3)/6
Therefore the probability that the coin lands on heads is D = (3±√3)/6
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which number line shows -4, -1, 1, and 2 correctly plotted.
A number line which shows -4, -1, 1, and 2 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical values -4 and -1 would be plotted on the left hand side of zero (0) while the numerical values 1 and 2 would be plotted on the right hand side of zero (0) using a number line.
In this scenario, a number line would be used for the comparison of two or more numbers such as -4, -1, 1, and 2, and this is plotted in the graph shown in the image attached below.
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Simplify each expression.
1) 7w + 2w - 6w
2) 9x - 3x + 2x 3) 8p + 3p - p
4) 6b-3b+5b
The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.
The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.
Here, all the questions can be solved by using the BODMAS rule.
1) 7w + 2w - 6w
= (7w + 2w) - 6w
= 9w - 6w
= 3w.
2) 9x - 3x + 2x
= (9x + 2x) -3x
= 11x - 3x
= 8x.
3) 8p + 3p - p
= (8p + 3p) - p
= 11p - p
= 10p.
4) 6b - 3b + 5b
= (6b +5b) - 3b
= 11b -3b
= 8b.
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Step-by-step explanation:
[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]
[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]
[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]
[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]
2. One plane
points_____
passes through three noncollinear
A. Point, Line, and Plane Postulates do not
address this topic directly.
B. always
C. never
D. sometimes
An astronaut has an annual income of $161,141.00.
The income tax an astronaut must pay is 8%.
What is the amount of income tax in dollars and cents that the
astronaut must pay?
Find an equation for the perpendicular bisector of the line segment whose
endpoints are (6, -5) and (-2, -9)
The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.
What is standard form equation?Ax+By=C is the standard form for linear equations in two variables. 2x+3y=5, for example, is a standard linear equation. It is relatively simple to find both intercepts when an equation is given in this form (x and y).In mathematics, a number is written in standard form. The simplest form of decimal numbers is standard form, which can be easily read and written. The standard form of the decimal number 0.007, for example, is 7 10-3. It can be difficult to read or write very large or very small numbers at times. As a result, we write them in standard form.The standard form of numbers (also known as "scientific notation") has different meanings depending on where you are in the world.Therefore,
The coordinates of the end points:
(6, -5) and (-2, -9)
((6, -5) +(-2, -9))/2
= ((6,-9)/2, (-2, -5)/2)
= (1.5, 3.5)
The difference in endpoint coordinates will be;
(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)
Then the ratio of these values, so we need to divide both by the common factor of 2:
(Δx, Δy) = (7, 2)
A line perpendicular to this segment through the point (h, k) can be written as;
Δx·x +Δy·y = Δx·h +Δy·k
7x ,2y = 7(2) 2(4)
7x, 2y = 6 .
Hence the standard form equation for the perpendicular bisector will be; 7x ,2y = 6 .
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Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
As per the given percentage, Sherry want to invest $2,000 amount in mutual fund and $13,200 amount in bonds.
Percentage:
Percentage means the number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Given,
Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.
Here we need to find if she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account.
It is given that the total amount is 15200.
So, let us consider x be the amount invested in mutual funds then 15200 - x be the amount invested in bonds.
Therefore, it can be written in the following matrix,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}[/tex]
Now, we have know that the total interest amount after 1 year is 548,
So, it can be written like the following expression
amount invested x percentage = final amount
Therefore,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}\times\begin{bmatrix}\frac{1}{100} \\\frac{4}{100}\end{bmatrix}=548[/tex]
It can be simplified as,
[tex]\begin{bmatrix}x\times(\frac{1}{100})+(15200-x)\times(\frac{4}{100}) \end{bmatrix}=[548][/tex]
=> x/100 + 60800-4x/100 = 548
=> x + 60800 - 4x = 54800
=> -3x = 54800 - 60800
=> -3x = -6000
=> x = 2000
=> 15200 - 2000 = 13200
Therefore, she invests $2,000 in mutual funds and $13, 200 in bonds.
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The expansion of (2 px)^6 in ascending powers of x, as far as the term in x², is
64 + Ax + 135x²
Given that p > 0, find the value of p and the value of A.
Answer: [tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]
Step-by-step explanation:
64+Ax+135x^2
135x^2+Ax+64=0
[tex]x_{1,\:2}=\frac{-A\pm \sqrt{A^2-4\cdot \:135\cdot \:64}}{2\cdot \:135}[/tex]
[tex]x_{1,\:2}=\frac{-A\pm \left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]
[tex]x_1=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135},\:x_2=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]
[tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]
help meeeeeeeeeeeeeee pleaseee
The vertex of the graph is (2, -1), the axis of symmetry of the graph is x = 2 and the parabola opens downward
How to determine the properties of the function?The vertex
The graph represents the given parameter
From the graph, we can see that:
The maximum point on the graph is located at
(2, -1)
The vertex of a graph is the maximum or the minimum of the graph
This means that
Vertex = (2, -1)
The axis of symmetry
The graph represents the given parameter
In (a), we have
Vertex = (2, -1)
Remove the y-coordinate
x = 2
The axis of symmetry of a graph is the x coordinate of the vertex
This means that the axis of symmetry is x = 2
The direction of the parabolaFrom the graph, we can see that the parabola opens downward
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Help me please!!!!!
The matrix
[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
The given matrix is
[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]
[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]
The Order of M = (3×2)
The Order of N = (2×3)
Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,
The order of the matrix formed is MN = ( 3 × 3 )
So,
[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
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c) √6 x √6 x√6 can someone help
Answer:
14.7
Step-by-step explanation:
Answer:
6[tex]\sqrt{6}[/tex]
or
≈14.7
Step-by-step explanation:
√6 x √6 x√6 can someone help
√6 x √6 x√6 =
6[tex]\sqrt{6}[/tex]
or
≈14.7
A and B are two similar solids. 1A А 10 cm The volume of A is 400 cm³. Work out the volume of B. 15 cm B
The volume of solid B is 1350 [tex]cm^{3}[/tex].
What is the volume ratio?
The side length ratio raised to the third power represents the volume ratio for the two solids.
If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.
Given that both solids are similar.
The volume of solid A = 400 [tex]cm^{3}[/tex]
height of solid A = 10 cm
height of solid B = 15 cm
the volume of solid B = ?
Now,
volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3
or, [tex]\frac{400}{x} = \frac{10^{3} }{15^{3} }[/tex]
or, [tex]x = \frac{400*15^{3} }{10^{3}}[/tex]
or, [tex]x = \frac{400*3375 }{1000}[/tex] = 1350
Hence, the volume of solid B is 1350 [tex]cm^{3}[/tex].
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Someone help
Given the function f(x) = 1 + 1/2x³, find the value of f(-4) in simplest form.
Answer: -62.5
PLEASE GIVE BRAINLIEST THANK YOU!!!
Step-by-step explanation:
Two libraries donated books to a local school. One library donated 786 books and the other
library donated 1,245 books. The school divided the books evenly among 11 classrooms.
Estimate how many books each classroom received.
Choose 1 answer:
B
200 books
Donat
50 books
The number of books each classroom received = 185
In this question, we have been given two libraries donated books to a local school. One library donated 786 books and the other library donated 1,245 books. The school divided the books evenly among 11 classrooms.
We need to find the number of books each classroom received.
Total number of books received:
786 + 1245 = 2031
The school divided the books evenly among 11 classrooms.
Let x be the number of books each classroom received.
By unitary method,
x = 2031 /11
x ≈ 185
Therefore, the number of books each classroom received = 185
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4) Identify all the zeros that make the function
true. f(x) = 2x² - 8
0
-2
2
-4
4
-8
The zero of the function f(x) = 2x² - 8 is ± 2.
Zeros of the function
Zero of the function means the values of x when f(x) is equal to 0. Which means that when f(x) = 0, x is a zero of the function.
Given,
Here we have the function f(x) = 2x² - 8.
Here we need to find the zero of the function.
As per the definition of the zeros of the function,
We have to apply the value of f(x) = 0, then we get,
2x² - 8 = 0
Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,
2x² = 8
Now, move the number 2 to the right hand side then it will be dividing the number 8,
x² = 8/2
x² = 4
x = √4
Therefore, the value of x is ± 2.
So, the zeros of the function is either +2 or -2.
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13.ERROR ANALYSIS Describe and correct the error in
the student's reasoning.
Answer:
Step-by-step explanation:
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.
Step-by-step Explanation:
Given:
Formula:
[tex] \rm v = \sqrt{2gh} [/tex]
Where,
v = velocity (in feet per second)
h = Height fallen (in feet)
g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²
To find:
How far an object has fallen if its velocity (v) is 136 ft/s
Solution:
By substituting the value of g & v in the formula we get:
[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]
A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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