5.NF.2. Word Problems
Keith picked 2 {5}/{6} buckets of apples and Sandy picked 4{1}/{3} buckets. How many money buckets of apples did sandy pick?
Jayson has 2{1}/{2} months' worth of pay saved in his account. He has 1{1}/{4} months' worth of pay saved in cash. Altogether, how much money has Jayson saved?

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

Hi

Step-by-step explanation:

Good bye. ;) (Stranger-Danger!) :)

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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By the process of conversion of unit, it can be found that

Height of Michael in inches is 48 inches

Height of Michael in yards is 1.33 yards

What is conversion of unit?

Conversion of unit is the process in which the value of one unit can be converted into the value of another unit.

Conversion of unit is  very important especially in doing sums in physics or chemistry.

Here,

Michael is 4 ft tall

Now height of Michael in inches = \(12 \times 4\) inches

                                                  = 48 inches

Now, height of Michael in yards = \(4 \times \frac{1}{3}\) yards

                                                   = \(1.33\) yards

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The statement "When the sample means lies relatively far away from µ0 in a hypothesis test, the decision should be to reject the null hypothesis." is false

This is further explained below.

Generally, When the p-value is lower than or equal to your significance threshold, you should conclude that the null hypothesis is incorrect.

Your findings from the sample provide support to the alternative hypothesis, which indicates that the effect may be present in the population as a whole.

Remember, as a mnemonic device, that when the p-value is low, the null hypothesis must be discarded!

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Answer:

I'll be glad to assist you.

Step-by-step explanation:

Given f (x) = 3x^2 - 4x + 2; What is f (-5)

f (-5) = 3x^2 - 4x + 2

f (-5) = 3(-5)^2 - 4(-5) + 2

f (-5) = 3(25) - 4(-5) + 2

f (-5) = 75 + 20 + 2

f (-5) = 97

or

( -5 , 97 )

C=πd

r=21

d=42

C=132 ft, and D is your final answer. Hope it help!

Answer:

132

Step-by-step explanation:

D

Answer:

7 hours.

Step-by-step explanation:

$6 x 7 = $48

$48 - $7= $41

Answer:

75

Step-by-step explanation:

35+4x where x is 10

35+4*10

35+40

75

Answer:

75

Step-by-step explanation:

4 packs of balloons which each have 10 balloons is 40 total balloons she bought. Add 40 to 35 which is 75.

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

It is correct please I do not want yo sound rude can you give me brainliest answer.

Answer:

correct steps

Step-by-step explanation:

if asked to find angles in terms of the ratios, then don't forget to shift sin / cos / tan across the equal sign and change it to arc sin / cos / tan.

Graphed f(x)=3sin(x) below in radians.

The time taken is 5.3 years.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P = 50, 000

W= 5000

r= 1.8%= 0.018

n= 2

Using, P = W (1- \((1+ r/n)^{-nt}\)) / (r/n)

Putting all the values we get

P = W (1- \((1+ r/n)^{-nt}\)) / (r/n)

50000 = 5000 (1- \((1+0.018/2)^{-2t}\)) / (0.018/2)

10 = (1- \((1+0.009)^{-2t}\)) / (0.009)

0.09 = 1 - \((1.009)^{-2t\)

\((1.009)^{-2t\) = 0.91

Taking log on both side

-2t log 1.009 = log 0.91

t= log 0.91/ (log 0.091) / (-20

t= 5.3

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Answer:

Step-by-step explanation:

Let the number be x .

Now ,

1 ) number is tripled : - 3x

2 ) result is decreased by 7 : - (3x - 7)

3 ) 3x  -  7  =  2 x -8

    3x  -  7  =  -16

    3x  =  -9

    x  =  -3

Answer:

College town race is 31% of the home town race.

Step-by-step explanation:

Length of hometown race = 3 miles

Length of college town race = 1492 meters

Since 1 meter = 0.0006214 miles

Therefore, 1492 = 0.93 miles

Percentage of college town race to the hometown race,

= \(\frac{\text{College town race}}{\text{Home town race}}\times 100\)

= \(\frac{0.93}{3}\times 100\)

= 31%

Therefore, the college town race is 31% of the home town race.

Answer:

the answer is the first one.

Step-by-step explanation:

Answer:

b: It is a product, so it is released by the plant.

Step-by-step explanation:

good luck

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

An individual who spent 30 minutes weight lifting will burn approximately 142.4768 calories.

Step-by-step explanation:

Given;

yˆ = 8.6067x + 116.6567 ............................... (1)

Where;

yˆ = The average number of calories burned by a 160 lb individual

x = Amount of time spent weight lifting

Since x is amount of time spent weight lifting, this implies that for an individual who spent 30 minutes weight lifting, x = 30

Substituting x = 30 into equation (1), we have:

yˆ = (8.6067 * 30) + 116.6567

yˆ = 25.8201 + 116.6567

yˆ = 142.4768

Therefore, an individual who spent 30 minutes weight lifting will burn approximately 142.4768 calories.

Answer: 11

Step-by-step explanation:

6+27=33

33/3 = 11

There are 13 cards of each suit.

Picking a heart would be 13/52 which reduces to 1/4

Then replacing the card and picking a club would be the same : 1/4

Picking a heart then a club would be 1/4 x 1/4 = 1/16

Answer: 1/16

The percentage of increase in her score is 6.82%

Here we will define her first score, 88, as the 100%.

So we can write the relation:

88 = 100%.

Her next score is 94, this will be a percentage X, then we can write:

94 = X

Taking the quotient between the two equations:

94/88 = X/100%

Solving this for X we get:

(94/88)*100% = X = 106.82%

The difference between the percentages gives the increase:

106.82% - 100% = 6.82%

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Answer:

\(\Large \boxed{\sf 384 \ m^2}\)

Step-by-step explanation:

Surface area ⇒ area of 2 triangles + area of 3 rectangles

\((8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384\)

Answer:

Surface Area = 384 m²

Step-by-step explanation:

The given figure is a triangular prism.

The surface area of a triangular prism is made up of:

From inspection of the diagram, the dimensions of the triangular bases are:

\(\boxed{\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of triangular base}&=\dfrac{1}{2} \times 8 \times 3\\&=4 \times 3\\&=12\; \sf m^2 \end{aligned}}\)

From inspection of the diagram, there are two congruent rectangles with dimensions:

and one rectangle with dimensions:

\(\boxed{\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\\\\implies \textsf{Area of rectangle 1}&=5 \times 20\\&=100\; \sf m^2 \\\\\implies \textsf{Area of rectangle 2}&=8 \times 20\\&=160\; \sf m^2\end{aligned}}\)

Therefore, the total surface area of the given triangular prism is:

\(\begin{aligned}\textsf{Total Surface Area}&=\sf 2\;Triangles + 2\;Rectangle\;1+Rectangle\;2\\& = 2 \times 12+ 2 \times100+160\\& = 24+200+160\\& = 224+160\\& = 384\; \sf m^2\\\end{aligned}\)

9514 1404 393

Answer:

  1. f^-1(x) = 4/(x+2) -2

  2. f^-1(x) = (-(x+3)/2)^(1/5)

Step-by-step explanation:

1. As with all "inverse function" problems, solve for y:

  x = f(y)

  x +2 = 4/(y +2) . . . . add 2

  y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)

  y = 4/(x+2) -2 . . . . . subtract 2

We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.

  f^-1(x) = 4/(x+2) -2

__

2. x = f(y)

  x +3 = -2y^5 . . . . add 3

  -(x +3)/2 = y^5 . . . . . divide by 2

  (-(x +3)/2)^(1/5) = y . . . . take the 5th root

  f^-1(x) = (-(x +3)/2)^(1/5)

In typeset form, that is ...

  \(\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}\)

This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.

_____

The graphs show the function and inverse are symmetrical about the line y=x, as they should be.

The correct option A: y = -4 cos Ф/4, is the cosine function for the graph.

The ratio between the angle's adjacent leg and the hypotenuse when it is regarded as a leg of a right triangle is a trigonometric function for an acute angle.

For the given graph,

cosine function:  y = -4 cos Ф/4.

In which, -4 is the amplitude (maximum displacement from the x axis).

Negative sign shows, the displacement is taken along negative y-axis.

And,  Ф/4 is the phase angle.

Thus, the cosine function for the graph is  y = -4 cos Ф/4.

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Answer:

b. \(\displaystyle y = -4cos\:4\theta\)

Step-by-step explanation:

\(\displaystyle y = 4cos\:(4\theta \pm \pi) \\ \\ \\ y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from \(\displaystyle [0, -4]\) instead of downward from \(\displaystyle [0, 4],\) telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [0, -4],\)from there to \(\displaystyle [-\frac{\pi}{2}, -4],\) they are obviously \(\displaystyle \frac{\pi}{2}\:unit\)apart, telling you that the period of the graph is \(\displaystyle \frac{\pi}{2}.\) Now, as you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4cos\:4\theta.\) Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted \(\displaystyle \frac{\pi}{4}\:unit\) on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.\)So, one equation of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = 4cos\:(4\theta \pm \pi).\) Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is \(\displaystyle y = -4cos\:4\theta.\) Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\) in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

9514 1404 393

Answer:

  no solutions

Step-by-step explanation:

Subtract the second equation from the first:

  (y -13) -(y -5x) = (5x) -(12)

  5x -13 = 5x -12 . . . . . . simplify

  0 = 1 . . . . . . . . . . . . . . .add 13-5x to both sides

No value of the variable will make this statement true.

There is no solution.