Answer:
20 ft
Step-by-step explanation:
The right triangles formed by Lance and his shadow and the tree and it's shadow are similar, hence the ratios of corresponding sides are equal.
Let the height of the tree be h, then
[tex]\frac{5}{h}[/tex] = [tex]\frac{8}{32}[/tex] = [tex]\frac{1}{4}[/tex]
cross- multiply to obtain
h = 5 × 4 = 20
The height of the tree is 20 ft
Answer:
20 feet
Step-by-step explanation:
5 feet Object = 8 feet shadow
8 feet shadow = 5 feet Object
8 feet shadow = 5 feet Object
1 foot shadow = 5 ÷ 8 = 5/8 foot object
1 foot shadow = 5/8 foot object
32 feet shadow = 5/8 x 32 = 20 feet object
What is the recursive formula for this sequence 12,16,20,24,28
I think it’s 12 table I believe
ANSWER
The recursive formula is
[tex]a_n = a_ {n - 1}+ 4[/tex]
EXPLANATION
The given sequence is 12,16,20,24,28
The first term of this sequence is
[tex]a_1=12[/tex]
The common difference is
d=16-12
d=4
The recursive formula is given by
[tex]a_n = a_ {n - 1}+ d[/tex]
So we need to substitute the known values to get
[tex]a_n = a_ {n - 1}+ 4[/tex]
what is 9!
the exclamation point is supposed to be there
Answer:
362880
Step-by-step explanation:
9! is read as 9 factorial.
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9! = 362880
Answer:
362,880
9! is also know as 9x all the numbers lower then it, so it would be 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
If you multiply all of those digits together, your result would be 362,880.
NEED HELP ASAP!! Find the indicated side of the trinagle
Answer:
b = 8sqrt(3)
Step-by-step explanation:
The triangle has a 30-deg angle and a right angle, so the third angle measures 60 degrees making this a 30-60-90 degree right triangle.
You don't mention which method to use to solve the problem.
You can use trigonometry ratios or the ratios of the lenghts of the sides of a 30-60-90 triangle
I'll use the second method.
In a 30-60-90 triangle, the lengths of the sides are in the ratio:
1 : sqrt(3) : 2
The long leg measures 12 and corresponds to sqrt(3) in the ratio, so we can find the length of the short leg by dividing 12 by sqrt(3).
12/sqrt(3) = [4 * sqrt(3) * sqrt(3)]/sqrt(3) = 4sqrt(3)
The hypotenuse is twice the length of the short leg.
b = 2 * 4sqrt(3) = 8sqrt(3)
The value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle shown in the picture.
From the cos ratio:
cos30 = 12/b
b = 12/cos30
b = 12/(√3/2)
After factorization:
b = (24√3)/3
b = 8√3
Thus, the value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
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Examine today’s stock listing for Parchar Special Effects, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 160.44 81.91 PCR 7.55 114.36 -4.89 Based on this information, what was yesterday’s price for Parchar Special Effects? a. $114.36 b. $109.47 c. $106.81 d. $119.25
Answer:
D
Step-by-step explanation:
I just took the test on E2020
Answer:
Option D. $119.25
Step-by-step explanation:
Today's stock listing for Parchar Special Effects shown below.
52 wk high = 160.44
52 wk low = 81.91
Symbol = PCR
Div. = 7.55
Close = 114.36
Net change = -4.89
Based on this information today's close is $114.36 and Net change is -4.89. It means the value of yesterday was 4.89 more than today's close.
Therefore, yesterday's price = 114.36 + 4.89 = $119.25
Yesterday's price was $119.25.
If a 40 foot tree cast a 12 foot shadow find the length of the shadow cast by a 27 foot tree
Answer:
8.1 ft
Step-by-step explanation:
We can use proportions to solve. Put the height over the shadow
40 ft 27 ft
---------- = -----------
12 ft x ft
Using cross products
40x = 12*27
40x =324
Divide each side by 40
40x/40 = 327/40
x = 8.1
The shadow is 8.1 ft
4y+3y+8-5 simplify Plz help meh!
7y+3
combine like terms.
Hey there!
4y + 3y + 8 - 5
COMBINE the LIKE TERMS
= (4y + 3y) + (8 - 5)
= 4y + 3y + 8 - 5
= 7y + 3
Therefore, your answer is: 7y + 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Vanessa practices the piano for 60 minutes each day. So far, she has practiced 42 minutes today. What percent of her practice time does she have left to complete?
Answer:
30%
Step-by-step explanation:
1) Find the amount of time left to complete
60 minutes total - 42 minutes already played = 18 minutes left
2) Divide the amount of minutes left by the total minutes
18 minutes left ÷ 60 minutes total = 0.3
3) Multiply that value by 100 to turn the decimal into a percent
0.3 * 100 = 30%
Answer:
30%
Step-by-step explanation:
The answer is thirty percent. One way to solve this problem is to start by finding what percent of Vanessa’s practice time forty-two minutes represents.
Let p represent the unknown percent, and set up a proportion that compares the like ratios of parts to wholes.
Divide out the like minutes and cross multiply.
Divide both sides by sixty to solve for the percent of time Vanessa has already practiced.
Subtract seventy percent from one hundred percent to determine the percent of time she has left to practice.
Vanessa still has thirty percent of her practice time to complete.
what is the cube root of 8x^27?
Answer:
2x^9
Step-by-step explanation:
∛8x^27
=∛(2x^9)^3
= 2x^9
Cube root of 8x^27 = 512.
How the cube root of 8x^27 is 512?In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots.
∛8x^27
=∛(2x^9)^3
= 2x^9
= 512.
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Explain why the triangles are similar, then find the value of x.
Answer:
ANSWER: D AA, x = 5 1/3
Calculation:
x/8 = 10/15
x = (10/15)(8)
x = 5 1/3
Step-by-step explanation:
Answer: AA postulate
Step-by-step explanation:
find the component form of -u - v given that u=(-3,5) and v =(6,-3)
ANSWER
B.
[tex] < \: - 3, -2 \: > [/tex]
EXPLANATION
The given vectors are:
[tex]u = < \: - 3,5 \: > [/tex]
and
[tex]v= < \: 6, - 3\: > [/tex]
[tex] - u - v = - 1< \: - 3,5 \: > -1 < \: 6, - 3\: > [/tex]
Use the scalar to multiply and obtain;
[tex] - u - v = < \: 3, - 5 \: > + < \: - 6, 3\: > [/tex]
Simplify to get:
[tex]- u - v = < \: 3 - 6, - 5 + 3 \: > [/tex]
[tex]- u - v = < \: - 3, -2 \: > [/tex]
To find the component form of -u - v, subtract the x-components and y-components separately. The x-component is 3, and the y-component is -2.
Explanation:The component form of -u - v can be found by subtracting the x-components and the y-components of u and v separately. Given that u=(-3,5) and v =(6,-3), the x-component of -u - v is -(-3) - 6 = -3 + 6 = 3, and the y-component is -(5) - (-3) = -5 + 3 = -2.
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If you create a box-and-whisker plot for the data set, which expression correctly calculates the third quartile, Q3, of the data set?
{4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.6, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4}
A)
(4.6 + 4.9)
2
B)
(4.5 + 5.1)
2
C)
(4.6 + 4.8)
2
D)
(4.4 + 4.8)
2
Answer:
D or "(4.4 + 4.8)
_______
2
Step-by-step explanation: I got it right on USA Test Prep
Find the value of n .
6/n = 24/28
y = ___.
Answer:
[tex]n=7[/tex]
Step-by-step explanation:
Cross multiply, isolate the variable, and divide by the coefficient to solve.
[tex]\frac{6}{n}=\frac{24}{28} \\ \\ 24n=168 \\ \\ n=7[/tex]
Plug back in to check.
[tex]\frac{6}{7}=0.857142857 \\ \\ \frac{24}{28} =0.857142857[/tex]
Answer:
7
Step-by-step explanation:
I did it and it was correct! Please make me brainliest!
Hope this helpd! :)
What is the slope of the line between points A(-3,4) and B(2,-7)?
Answer:
I made the problem in a photo so you could do it for the next
Rise is the change between the y-coordinates of any two points along a line in the xy-plane. True or False
Rise is the change between the y-coordinates of any two points along a line in the xy-plane. True or False
The rise is the change between the y-coordinates of any two points along a line in the xy-plane is true.
What are rise and run?In a graph, the terms "rise" and "run" refer to the vertical and horizontal changes between two points on a line, respectively.
Here,
The rise of a line in the xy-plane is the vertical change between two points on the line, which is measured as the difference between their y-coordinates. The rise is sometimes also called the vertical distance or the vertical change.
Thus, the rise is the change between the y-coordinates of any two points along a line in the xy-plane is true.
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Solve for y: 6x-3y=24
Answer:
[tex]y=2x-8[/tex]
Step-by-step explanation:
Isolate the variable and divide by the coefficient to solve for a variable.
[tex]6x-3y=24 \\ \\ -3y=-6x+24 \\ \\ y=2x-8[/tex]
Answer:
y = 2x - 8
Step-by-step explanation:
=> 6x - 3y = 24
=> -3y = 24 - 6x
=> 3y = 6x - 24
=> y = 2x - 8
Based on the tree diagram below, what is the probability that a student doesn't have lice, given that the student tested negative? Round your answer to the nearest tenth of a percent.
A. 97.6%
B. 99.4%
C. 96.4%
D. 98.6%
Answer:
Option D (APEX)
Step-by-step explanation:
L= Student has lice
NL= Student has no lice
PT=Test Shows positive
NT=Test Shows negative
P([tex]\frac{NT}{NL}[/tex]) =0.7708 (Probability that a student has no lice and the test shows negative)
P([tex]\frac{NT}{L}[/tex]) = 0.0108 ( Probability that a student has lice and the test shows negative)
[tex]P\frac{NT}{NL}[/tex] = [tex]\frac{P\frac{NT}{NL} }{P\frac{NT}{NL} +P\frac{NT}{L} }[/tex][tex]\frac{0.7708}{0.7708+00108}[/tex][tex]\frac{0.7708}{0.7816}[/tex]0.98618219 (Simplify)Terms Of Percentages
0.98618219 × 100
=98.6
Therefore your answer is 98.6% (Option D)
APEX
The probability that the student doesn't have lice, given that the student tested negative is P ( A ) = 98.6 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the student doesn't have lice, given that the student tested negative be P ( A )
Now , the equation will be
The probability that a student has no lice and the test shows negative is given by P ( NL ) = 0.7708
The probability that a student has lice and the test shows negative is given by P ( L ) = 0.0108
And , The probability that the student doesn't have lice, given that the student tested negative P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]
On simplifying , we get
P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]
P ( A ) = ( 0.7708 ) / [ 0.7708 + 0.0108 ]
P ( A ) = 0.98618
P ( A ) = 98.6 %
Hence , the probability is 98.6 %
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area of circle
area
inscribed polygon
polygon
perimeter
equilateral
length
octagon
trapezoid
apothem
legs
hexagon
circle
composite figure
regular polygon
Answer:
1. area
2. circle
3. equilateral
4. length
5. perimeter
6. polygon
7. regular polygon
8. trapezoid
9. legs
10. area of a circle
11. hexagon
12. octagon
13. inscribed polygon
14. apothem
15. composite figure
Step-by-step explanation:
Triangle ABC was dilated using the rule Do.4. Triangle
A'B'C' is the result of the dilation
what is OB'?
1.5 units
3 units
4.5 units
6 units
Answer:
The correct option is B. The length of OB' is 3 units.
Step-by-step explanation:
The rule of dilation is D₀,₄. It means dilation by scale factor 4 with center of dilation is origin.
[tex]\text{Scale factor}=\frac{\text{Distance between center and any point of the image}}{\text{Distance between center and corresponding point of the Preimage}}[/tex]
[tex]\text{Scale factor}=\frac{OB'}{OB}[/tex]
[tex]4=\frac{OB'}{\frac{3}{4}}[/tex]
[tex]4\times \frac{3}{4}=OB'[/tex]
[tex]3=OB'[/tex]
The length of OB' is 3 units. Therefore the correct option is option is B.
Answer:
B on edge
Step-by-step explanation:
What is Brenda z-score
The z-score formula is:
x - mean / standard deviation
x = her height.
Z-score = (50 - 49) / 2
z-score = 1/2 = 0.5
What type of triangle has exactly two acute angles?
right
obtuse
equilateral
acute
Answer:
right and obtuse
Step-by-step explanation:
a right triangle has one right angle and two acute angles, and an obtuse triangle has one obtuse angle and two acute ones
i hope that this helps :)
Over 2 years, how much more does $2000 in a savings account with an APR
of 4.6% compounded semiannually earn in interest than the same amount in
a savings account with an APR of 4.4% compounded quarterly?
Answer:
Final answer is $7.52.
Step-by-step explanation:
Given that initial amount P = $2000
Interest rate r = 4.6% = 0.046
Number of compounding periods per year = n = 2 {semiannually}
Time = 2 years
Then future value is given by :
[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]
[tex]A=2000\left(1+\frac{0.046}{2}\right)^{2\left(2\right)}=2190.45[/tex]
Similarly calculate future value for 2nd case:
Given that initial amount P = $2000
Interest rate r = 4.4% = 0.044
Number of compounding periods per year = n = 4 {quarterly}
Time = 2 years
Then future value is given by :
[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]
[tex]A=2000\left(1+\frac{0.044}{4}\right)^{4\left(2\right)}=2182.93[/tex]
then difference = 2190.45 - 2182.93 = 7.52
Hence final answer is $7.52.
Answer:
$7.52
Step-by-step explanation:
look at the picture and plzzz help
the answer to the problem would be c
ANSWER
The correct choice is C.
EXPLANATION
We know that:
[tex] \sqrt[3]{7} = {7}^{ \frac{1}{3} } [/tex]
We want to simplify:
[tex]( { {7}^{ \frac{1}{3} } )}^{3} [/tex]
The exponent here is 3. This means that the base must multiply itself 3 times.
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
This implies that,
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} } [/tex]
Simplify:
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{3}{3}} [/tex]
[tex]( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ 1} = 7[/tex]
The correct choice is C
solve log8 12=x-2. Round your answer to four decimal places.
Answer:
[tex]\large\boxed{x\approx3.1950}[/tex]
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\\log_812=x-2\iff8^{x-2}=12\\\\(2^3)^{x-2}=4\cdot3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(x-2)}=2^2\cdot3\qquad\text{use the distributive property}\\\\2^{3x-6}=2^2\cdot3\qquad\text{divide both sides by}\ 2^2\\\\\dfrac{2^{3x-6}}{2^2}=3\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\2^{3x-6-2}=3\\\\2^{3x-8}=3\qquad\text{logarithm of both sides}\\\\\log_22^{3x-8}=\log_23\qquad\text{use}\ \log_aa^n=n\\\\3x-8=\log_23\qquad\text{add 8 to both sides}[/tex]
[tex]3x=\log_23+8\qquad\text{divide both sides by 3}\\\\x=\dfrac{\log_23+8}{3}\\\\\log_23\approx1.5849625\\\\x\approx\dfrac{1.5849625+8}{3}\approx3.1950[/tex]
Answer:
B
Step-by-step explanation:
edge 2020
Given that C=3 and d=2, What is the value of x if x=2C+d
Answer
2(3)=6 + 2 = 8
The value of x will be;
⇒ x = 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
C = 3 and d = 2,
And, The equation is,
⇒ x = 2C + d
Here,
The values are,
⇒ C = 3 and d = 2,
Substitute above value in equation , we get;
⇒ x = 2C + d
⇒ x = 2 × 3 + 2
⇒ x = 6 + 2
⇒ x = 8
Thus, The value of x = 8.
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look at the picture and plzz give me the correct answer
Answer: C
Step-by-step explanation:
The initial amount of trees planted is 1,500, so answers B and D are out. The number that is raised to years (t) is 1.02, and since 1.02 is greater than 1, the number of trees planter per year is growing, and the .02 means that it is growing at 2% because 0.02 * 100 = 2%
Answer:
Step-by-step explanation:
C is correct. The initial number (of trees) was 1500, and that 2% translates into 1.02 inside the parentheses.
It is well known that Becky won an award for her 88 popular songs. what is Less well known, however, is that she wrote a total of 410 songs in her career. How many songs did Becky write that were not popular
Answer:
322 Unpopular songs
Step-by-step explanation:
If Becky has 88 total popular songs, and she wrote a total of 410 songs, it is simply subtracting her popular songs from her total songs.
410 - 88 = 322
Write and simplify a rational expression for the ratio of the perimeter to the area of rectangle if the width is 4x and the length is x+6
Answer:
5x + 6 : 2x² + 12x
Step-by-step explanation:
Width = 4x
Length = x + 6
Perimeter
= 2(4x + x + 6)
= 2(5x + 6)
Area
= 4x(x + 6)
Ratio of perimeter to area:
= 2(5x + 6) : 4x(x + 6)
= (5x + 6) : 2x(x + 6)
= 5x + 6 : 2x² + 12x
Answer:
(5x + 6) : (2x² + 12x)
Step-by-step explanation:
Perimeter = 2(length + width)
= 2[4x + x + 6]
= 2(5x + 6)
Area = length × width
4x × (x + 6)
4x(x + 6)
Perimeter : Area
2(5x + 6) : 4x(x + 6)
(5x + 6) : (2x² + 12x)
A basketball team has five players how many different teams can be formed from 15 people if position doesn't matter
Answer: 15•5= 75
Step-by-step explanation:
Express 18^1/2 in simplest radical form
The simplified form of 18^1/2 is 3√2
Radical expressions and indicesGiven the exponential expression
18^1/2
According to power law of Indices:
a½ = \sqrt{a}
Applying this law to the given expression;
This can also be written as:
[tex]18^{1/2} =\sqrt{18}[/tex]
Simplify the radical to have:
[tex]\sqrt{18} = \sqrt{9 \times 2} \\\sqrt{18} = 3\sqrt{2}[/tex]
Hence the simplified form of 18^1/2 is 3√2
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Please help i don't have alot time
Answer:
[tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=-2\sqrt{x-3}+8[/tex].
Now let's find it's range.
we know that square root function always gives positive output then:
[tex]\sqrt{x-3}\ge0[/tex]
[tex]-2\sqrt{x-3}\le-2\left(0\right)[/tex]
[tex]-2\sqrt{x-3}\le0[/tex]
[tex]-2\sqrt{x-3}+8\le0+8[/tex]
[tex]-2\sqrt{x-3}+8\le 8[/tex]
[tex]f(x) \le 8[/tex]
Hence range of the function is [tex](-\infty,8][/tex].
we can repeat same process to find the range of all the given choices.
we will find that only 3rd choice has same range.
Hence final answer is [tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]