Answer:
d = 240 - 44t
Step-by-step explanation:
Distance of the raft to the waterfall
The raft is heading for the waterfall, therefore, the distance between the raft and the waterfall is diminishing.
Waterfall=240 ft from the tunnel
Speed of the raft =44 ft per second
Therefore the equation of a function rule that represent the distance of the raft to the waterfall is:
d = 240 - 44t
Where t=time in seconds
How many points are needed to define a plane?
Answer:
3
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
5
Please answer this question now
Answer:
Approximately 439.6 square millimeters.
Step-by-step explanation:
The formula for the surface area of a cone is the following:
[tex]A=\pi r^2+\pi r l[/tex]
Where, r is the radius and l is the slant height.
The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:
[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]
Answer:
292.77
Step-by-step explanation:
πr(r+[tex]\sqrt{h2+r2}[/tex])
13 x 2 = 26
7 x 2 = 14
26 + 14 = 40
[tex]\sqrt{40}[/tex] = 6.32
7 + 6.32 = 13.32
3.14 x 7 = 21.98
21.98 x 13.32 =
292.77
Edward has four pearls – two white and two black – which he can distribute as he chooses between two identical bags. He must then choose a bag at random and pick one pearl at random from the bag he chose. If Edward distributes the pearls so as to maximize his chances of picking a black pearl, what is the probability that Edward will pick a black pearl?
Answer:
2/3
Step-by-step explanation:
Bag A: WWB
Bag B: B
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠W ≅ ∠C ∠W ≅ ∠D ∠W ≅ ∠A
Answer:
The Answer would be ∠W ≅ ∠C
Step-by-step explanation:
Only one that is congruent
The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
A triangle is a three-sided polygon with three edges and three vertices in geometry.
Given that the triangle ∆MTW is congruent to the triangle ∆CAD.
So, we have
∠MTW ≅ ∠CAD
∠WMT ≅ ∠DCA
∠TWM ≅ ∠ADC
If two triangles are equivalent, the ratio of matching sides will stay constant.
The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.
Therefore, at that point, the right choice is B.
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Show that the rational numbers -15/35 and 4/(-6) are not equal?
Answer:
-15÷35 is different from 4÷-6
Step-by-step explanation:
-15÷35=-3/7
4÷-6=-2/3
-3/7 is different from -2/3
1/3(12-6x)=4-2x I need help pls
Answer:
no solution
Step-by-step explanation:
1/3(12-6x)=4-2x
4-1.3x=4-2x
4=4-0.7x
0=0.7x
ns
What are the lower quartile, upper quartile, and median for this box and
whisker plot?
A) LQ = 22 UQ = 10 Median = 18.5
B) LQ = 10 UQ = 22 Median = 18
C) LQ = 10 UQ = 22 Median = 18.5
D) LQ = 10 UQ = 22 Median = 19
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lower quartile range is shown by the bottom of the box which is at 10.
The median is shown in the middle line, which is closer to 18 than 18.5.
The upper quartile range in the end of the box, which is at 22!
(You can also look at the picture attached if that helps.)
please this urgent!!
Answer:
Step-by-step explanation:
1)First convert mixed fraction to improper fraction and them prime factorize
[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]
[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]
2)
[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]
3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]
4) 144 = 12 * 12
12 = 6*2
6 = 2*3
Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2
= 2⁴ * 3²
5) To find LCM, prime factorize 96 & 144
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3
144 = 2⁴ * 3²
LCM = 2⁵ * 3² = 32 * 9 = 288
6) HCF
105 = 7 * 5 * 3
135 = 5 * 3* 3 * 3
180 = 5 * 3 * 3 * 2 * 2
HCF = 5 * 3 = 15
7) 24 = 3 * 2 * 2 * 2 = 3 * 2³
36 = 3 * 3 * 2 * 2 = 3² * 2²
40 = 5 * 2 * 2 * 2 = 5 * 2³
LCM = 5 * 2³ * 3² = 5 * 8 * 9 = 360
HCF = 2² = 4
Difference = 360 - 4 = 356
8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all
1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15
Ans: 15
9) 36₇ = 102₅
10) 6.9163 = 6.916
I knew only this much
hope it's helpful
:)
In a family with children, the probability that all the children are girls is appoximately . In a random sample of 1000 families with children, what is the approximate probability that or fewer will have girls? Approximate a binomial distribution with a normal distribution.
Answer:
The probability that 100 or fewer will have 3 girls is 0.00734.
Step-by-step explanation:
The complete question is:
In a family with 3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with 3 children, what is the approximate probability that 100 or fewer will have 3 girls? Approximate a binomial distribution with a normal distribution.
Solution:
Let X represent the number of families who has 3 girls.
The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.
But the sample selected is too large.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 10
2. n(1 - p) ≥ 10
Check the conditions as follows:
[tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]
The mean and standard deviation are:
[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]
Compute the probability that 100 or fewer will have 3 girls as follows:
Apply Continuity correction:
[tex]P(X\leq 100)=P(X<100-0.50)[/tex]
[tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]
*Use a z-table.
Thus, the probability that 100 or fewer will have 3 girls is 0.00734.
Sue likes to run. One day she was running for 3 hours with an average speed of 7 miles per hour. How many miles did she run that day?
Answer:
21 miles
Step-by-step explanation:
Since every single hour she runs 7miles.
In 3 hours she will run 7*3 miles.
21 miles
Hey there! I'm happy to help!
If Sue ran with an average speed of 7 miles an hour for 1 hour, she would have run 7 miles. So, if she ran at this speed for 3 hours, she would have run 3 times the distance she would if she ran for one hour!
7×3=21
Therefore, Sue ran 21 miles that day.
Have a wonderful day! :D
A Food Marketing Institute found that 31% of households spend more than $125 a week on groceries. Assume the population proportion is 0.31 and a simple random sample of 373 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.33
Answer:
0.7967
Step-by-step explanation:
We know that population proportion p=0.31.
We have to find P(phat<0.33).
Mean=p=0.31
[tex]Standard deviation=\sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]Standard deviation=\sqrt{\frac{0.31(0.69)}{373} }[/tex]
standard deviation=0.024 (rounded to three decimal places)
[tex]P(phat<0.33)=P(Z<\frac{0.33-0.31}{0.024})[/tex]
[tex]P(phat<0.33)=P(Z<\frac{0.02}{0.024})[/tex]
[tex]P(phat<0.33)=P(Z<0.83)[/tex]
[tex]P(phat<0.33)=0.5+0.2967[/tex]
[tex]P(phat<0.33)=0.7967[/tex]
Thus, the required probability that sample proportion of households spending more than $125 a week is less than 0.33 is 79.67%
The sum of two consecutive odd integers is at least 36, find the integers
Answer:
The two integers are greater than or equal to 17 and 19
Step-by-step explanation:
Consecutive odd integers means 1, 3, 5, 7, 9 and so on
That means there is a always a gap of 2 in between each of them. Knowing this, we can set up an equation. Let x represent the first of the consecutive integers.
x+(x+2)=36
x+2 represents the second consecutive interger
x+x=34
2x=34
x=17
The two integers are 17 and 19
SP=2x+3, and LN=5x−14. Find SP.
Answer:
43
Step-by-step explanation:
Using Thales theorem:
● SP/LN = RP /RN
Notice that RN = 2×RP
● SP/LN = RP/2RP
● SP /LN = 1/2
● SP / (5x-14) = 0.5
● (2x+3)/(5x-14) = 0.5
● 2x+3 = 0.5(5x-14)
● 2x+3 = 2.5x -7
Add 7 to both sides
● 2x+3+7 = 2.5x-7+7
● 2x+10 = 2.5x
Sustract 2x brom both sides
● 2x+10-2x = 2.5x-2x
● 10 = 0.5x
Multiply both sides by 2
● 10×2 = 0.5x×2
● 20 = x
Replace x with 20 in Sp expression:
● SP = 2x+3
● SP = 2×20+3
● SP = 43
Simplify:
[tex] \sqrt[4]{6 ^{4} } [/tex]
Answer:
6
Step-by-step explanation:
Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:
6^(4*1/4) = 6^1 = 6
Hope this helps!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each value to the correct expression.
The answer is shown below:
What is expression?An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.
1+5.2 + (1+3)²
=1+10 + 16
=27
0.25*4³-1
=0.25*64-1
=16-1
=15
4+8(1/4+2)
=4+8(9/4)
=4+2*9
=4+18
=22
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Chantal is driving on a highway at a steady speed. She drives 55 miles every hour. Let d be the total distance in miles and let h be the number of hours.
Write an equation that represents the situation. I'll give out the brainliest if you get it right.
Answer:
[tex] d = 55h [/tex]
Step-by-step explanation:
We are given that Chantal drives at a constant speed of 55 miles per hour.
If, d represents the total distance in miles, and
h represents number of hours, the following equation can be used to express the given situation:
[tex] d = 55h [/tex]
For every hour, a distance of 55 miles is covered.
Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]
If h = 2, [tex] d = 55(2) = 110 miles [/tex].
Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.
For a quadratic function y = ax² + bx + c, suppose the constants a, b, and c are consecutive terms of a geometric sequence. Show that the function does not cut the x axis.
Hello, because of the geometric sequence we can say that:
[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]
So there is no real root, so the function does not cut the x axis.
Thank you
For the given quadratic function, the x-axis is not cut by the function because there is no true root.
What is a quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.
As per provided data in question,
α = b/a = c/b
c/a = (c × b)/(a × b) = (c/b) (b/a) = α²
For the equation,
ax² + bx + c = 0
x² + b/a(x) + c/a = 0
⇒ x² + ax + α² =0
Δ = b² - 4 ac = α² - 4α²
Δ = -3α² < 0, which means that no real root is there.
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f(x)=x^2 what is g(x)?
pls help me
Chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine. a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
Answer:
30.0g
Step-by-step explanation:
In order to determine the amount of each chemical to the nearest tenth of gram prior to computing the sum is shown below:
Like
10.357, 57 > 50, rounded to 10.4
12.062, 62 > 50, rounded to 12.1
7.506, 06 < 50, rounded to 7.5
Now
The Sum is
= 10.4g + 12.1g + 7.5g
= 30.0g
Hence, 30.0g medicine required to make in grams
Can someone please explain this to me? I don’t understand it at all.
Segment AB was added to segment BC to get segment AC
representing it as an equation,
AC = AB + BC.
Substitute the values in the equation which means you are going to find the value of x.
77 = x + 16 + 4x +11
77 = 5x + 27
(group like terms)
77 - 27 = 5x
50 = 5x
( divide both sides by 5 to make x stand alone)
50/5=5x/5
10 = x
therefore ,x = 10.
To prove that segment AB =26, place x in the statement
AB = x+16
AB=10+16
AB=26/
Solve for x: 3x-4=2x-10
Answer:
x = - 6
Step-by-step explanation:
3x - 4 = 2x - 10
3x -2x = 4 - 10
x = - 6
For the equation 3x-4=2x-10, the value of x is -6.
The given equation is 3x-4=2x-10.
x is the variable in the equation.
Plus and minus are operators.
To solve for x, subtract 2x from both sides:
3x-2x-4=2x-2x-10
x-4=-10
Add 4 on both sides:
x=-10+4
x=-6
Hence, the value of x is -6.
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The subject is operations on rational expressions.
The instructions are add or subtract the following expressions. Remember to find a common denominator when necessary. Reduce all answers to lowest terms.
Answer:
[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]
= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
Now we have done the denominators of each term of the expression equal.
Further we add the terms,
[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]
Now factorize the numerator of the fraction.
4x² + 14x - 18 = 2(2x² + 7x - 9)
= 2(2x² + 9x - 2x - 9)
= 2[x(2x + 9) - 1(2x + 9)]
= 2(x - 1)(2x + 9)
Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.
Please show your work. I will give brainliest to the right answer!
Answer:
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
Step-by-step explanation:
Given:
Focus of parabola: (-4, 6)
Directrix: y = 2
Required:
Equation for the parabola
SOLUTION:Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.
Where,
a = -4
b = 6
k = 2
Plug these values into the equation formula
[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]
[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
Solve the following formula for m v2=3Pmn
Answer:
m= 0 /(−3np+v2 )
Step-by-step explanation:
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 221(1.09) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2008? A. 19%; $479.99 million B. 19%; $240.89 million C. 9%; $404.00 million D. 9%; $440.36 million
Answer:
D. 9%, 440.36 million
Step-by-step explanation:
w = 221(1.09)t
9%, 440.36 million
how do you find the surface area of this triangular prism?
To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them
Answer:
Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]
Step-by-step explanation:Step 1: Find the surface area of the 2 triangles
[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]
Step 2: Find the surface area of the 3 rectangles
(6x7) x 3 = [tex]126cm^2[/tex]
Step 3: Add the 2 surface areas together
[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]
Therefore the surface area of the prism is [tex]159cm^{2}[/tex]
Identify a pattern and find the next number in the pattern.
-5, 1, 7, 13
Answer:
19
Step-by-step explanation:
The pattern is that it +6 every number.
-5 + 6 = 1
1 + 6 = 7
7 + 6 = 13
So the next number is 13 + 6 = 19.
EDIT - I can't add sorry.
Answer:
Step-by-step explanation:
This is an arithmetic sequence.
-5, 1 , 7 , 13 ,.....
First term = a = -5
Common difference = d = second term - first term
= 1 - [-5] = 1 + 5
= 6
Next term = previous term + d
= 13 + 6 = 19
nth term = a +(n-1)*d
= -5 + (n-1)*6
= -5 + 6n - 6 {add like terms}
= -5 - 6 + 6n
= -11 + 6n
Pattern: 6n -11
kinda confused buttttt anyone know this?
Answer:
Hey there!
The overlapping part is the product.
Thus, the product is 1/8.
Hope this helps :)
Please answer thanks!
Answer:
see explanation
Step-by-step explanation:
tan x = -1
[tex]x = tan^{-1}(-1)[/tex]
x = -45
tan x = 5
[tex]x = tan^{-1}(5)[/tex]
x = 78.69
Answer:
See below.
Step-by-step explanation:
So we want to find the solutions to the two equations:
[tex]\tan(x)=-1 \text{ and } \tan(x)=5[/tex]
I)
[tex]\tan(x)=-1\\x=\tan^{-1}(-1)[/tex]
Recall the unit circle. First, note that the number inside tangent is negative. Because of this, we can be certain that the x (in radians) must be in Quadrant II and/or IV (This is because of All Students Take Calculus, where All is positive in QI, only Sine is positive in Q2, only Tangent is positive in Q3, and only Cosine is positive in QIV. Tangent is negative so the only possible choice are QII and QIV).
From the unit circle, we can see that x=3π/4 is a possible candidate since tan(3π/4)=-1.
Since tangent repeats every π, 7π/4 must also be an answer (because 3π/4 + π = 7π/4). And, as expected, 7π/4 is indeed in QIV.
Therefore, for the first equation, the solutions are:
[tex]x=3\pi/4 \text{ and } 7\pi/4[/tex]
II)
For the second equation, there is no exact value for which tangent of an angle would be equal to 5. Thus, we need to approximate.
So:
[tex]\tan(x)=5\\x=\tan^{-1}(5)\\x=\tan^{-1}(5) \text{ and } \tan^{-1}(5)+\pi[/tex]
We got the second answer because, like previously, tangent repeats every π, so we only need to add π to get the second answer.
In approximations, this is:
[tex]x\approx1.3734 \text{ and } x\approx4.5150[/tex]
Note: All the answers are in radians.
Am I doing this right if not please help me
Answer:
Step-by-step explanation:
For the m it would just be -3 because the equation for slope intercept form is y=mx+b
