Use ratios to convert each measurement.

1. 3 yards = _____ feet
2. _____ cups= 5 gallons
3. 72 inches =_____ yards
4. ______ ounces = 5 pounds
5. ______ inches =7 feet
6. 24 feet = _____ yards
7. 40 pints = ______ gallons
8. 16 cups = ______ quarts and
9. ________ inches = 4 yards
10. 48 ounces = ________ Pounds ​

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r   ==>   r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

Answer:

21.758

Step-by-step explanation:

If you draw the triangle out, you find that cos 41 = x/28.83, when x is equal to the side opposite the 49 angle

Simplify this into 28.83 cos 41, and plug it into the calculator and you get

21.75827.

Answer:

D. 16 years old

Step-by-step explanation:

Step 1: Let T be Tien's age and J as Jordan's age (today),

[tex]T=\frac{1}{4}J[/tex]

Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),

[tex]T+2=\frac{1}{3} (J+2)[/tex]

[tex]T=\frac{1}{3}(J+2)-2[/tex]

Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,

[tex]\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16[/tex]

Step-by-step explanation:

arranging in ascending order is simply arranging from the smallest to the largest.

12.4654,156.6100,267.0918,295.6097,784.7068

I hope this helps

• {4, 7, 12, 19, … }

has 1st differences

7 - 4 = 3

12 - 7 = 5

19 - 12 = 7

and 2nd differences

5 - 3 = 2

7 - 5 = 2

• {-1, 2, 7, 14, …}

1st differences:

2 - (-1) = 3

7 - 2 = 5

14 - 7 = 7

2nd differences:

5 - 3 = 2

7 - 5 = 2

• {-2, -8, -18, -32, …}

1st differences:

-8 - (-2) = -6

-18 - (-8) = -10

-32 - (-18) = -14

2nd differences:

-10 - (-6) = -4

-14 - (-10) = -4

Answer:

Hello,

Step-by-step explanation:

I  am  going to explain the method with the 1th:

[tex]\begin{array}{ccccc}n & u_n&u_{n+1}-u_{n}&u_{n+2}-2u_{n+1}+u_{n}&v_{n}\\1&4&&6\\2&7&3&9\\3&12&5&2&14\\4&19&7&2&21\\...&&&\\\end{array}\\\boxed{u_{n+2}=2u_{n+1}-u_{n}+2}\\[/tex]

[tex]Let\ say\\v_{n}=u_{n}+2\\v_{n+2}=u_{n+2}+2=(2u_{n+1}-u_{n}+2)+2=2(v_{n+1}-2)-(v{n}-2)+4\\v_{n+2}=2v_{n+1}-v{n}+2\ (1)\\v_{n+3}=2v_{n+2}-v{n+1}+2\ (2)\\(2)-(1)==> \boxed{v_{n+3}=3v_{n+2}-3v_{n+1}+v_n}\\[/tex]

[tex]Caracteristic\ equation:\\P(r)=r^3-3r^2+3r-1=0\\P(r)=(r-1)^3\\v_n=\alpha+\beta*n+\gamma*n^2\\v_1=6 ==> \alpha+\beta*1+\gamma*1=6\\u_2=9 ==> \alpha+\beta*2+\gamma*4=9\\u_3=14 ==> \alpha+\beta*3+\gamma*9=14\\[/tex]

[tex]\begin{bmatrix}1&1&1\\1&2&4\\1&3&9\end{bmatrix}*\begin{bmatrix}\alpha\\\beta\\\gamma\end{bmatrix}=\begin{bmatrix}6\\9\\14 \end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\1&2&4&9\\1&3&9&14\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&2&3&3\\0&2&8&8\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&1&4&4\end{bmatrix}\\\\[/tex]

[tex]\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&0&0\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&0&0&5\\0&1&0&0\\0&0&1&1\end{bmatrix}\\[/tex]

[tex]\alpha=5\\\beta=0\\\gamma=1\\\boxed{v_n=5+0*n+1*n^2}\\\boxed{u_n=5+0*n+1*n^2-2}\\\begin{array}{ccccc}n & u_n\\1&5+1-2=4\\2&5+4-2=7\\3&5+9-2=12\\4&5+16-2=19\\...&...\\\end{array}\\[/tex]

Answer:

-57

Step-by-step explanation:

the answer is -57 because if it is below sea level it is a negative but if it is above sea level it will be a positive

Answer:

horizontal analysis

Step-by-step explanation:

vertical analysis uses line items in the financial statements as a percentage of the base year which is the same as common size

ratio analysis compares line items between two companies against a base year.

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

Answer:

No

Step-by-step explanation:

Conditional probability is an event repeating itself.

ex.) you have 3 red marbles and 4 blue ones in a hat, since you already drew a red one, there is conditional probability you will draw red again. So unless you have already gotten a car for your birthday previously, you cannot classify your question as conditional probability.

Answer:

B IS THE MID POINT

Step-by-step explanation:

If b lies between AC iy means b is de half

therefore a+b+c=ABC which is the straight line

Answer:

Open in answr appOpen_in_app

(i)

15

7

=

30

x

⇒x=

15

7×30

=14

(ii)

3

x

=

18

12

⇒x=

18

12×3

=2

(iii)

x

30

=

24

45

⇒x=

45

30×24

=16

(iv)

16

8

=

x

25

⇒x=

8

25×16

=50

Step-by-step explanation:

yeah

Answer:

5

Step-by-step explanation:

May be correct than follow me please

Answer:

Step-by-step explanation:

The largest number must be less than 31.

The smallest number must be greater than 9.

Answer:

-2

Step-by-step explanation:

The output of the chart and graph drops by 2 for every input.

Answer:

P=61°

Step-by-step explanation:

P²=C²+ U²–2 C U cos P

189²= 215²+123²– 2×215×123×cos p

P= 61°

I hope I helped you^_^

Answer:

When you plot the graph, you may see a line or a curve. This presents the trend of the relationship of the two quantities when the independent variable changes.

Graphs visually depict patterns and trends, while equations provide precise mathematical descriptions, both revealing valuable information about the relationship between two quantities.

Graphs visually represent data and patterns, allowing us to identify the nature of the relationship between two quantities. The slope and intercepts of a graph provide information about the rate of change and the values when one quantity is zero.

Equations, on the other hand, offer precise mathematical descriptions of the relationship. The form of the equation reveals the nature of the relationship, while coefficients and constants provide specific information. Solving equations yields solutions that satisfy the relationship.

Both graphs and equations work together to provide a comprehensive understanding of the relationship between two quantities, with graphs offering visual insights and equations providing precise mathematical information.

Learn more about equations here;

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[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

Answer:

26 cm

Step-by-step explanation:

The area of a trapezium is

A = 1/2 (b1+b2)*h  where b1 and b2 are the lengths of the bases

910 = 1/2 ( 21+49) h

910 = 1/2 (70)h

910 = 35h

Divide by 35

910/35 = 35h/35

26 = h

Answer:

3×3×10^5×10^2

9×10^5-2

9×10³

Answer:

Below,...

Step-by-step explanation:

They are saying that if you add a odd number + a odd number than you'd get a even number,... odd + even = odd,... odd x even = even,... and so on,...

Hope it helps,... Chow!

Answer:

Step-by-step explanation:

h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m

The height of the building is 10 meters.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's call the height of the building "h".

We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:

h² + 24² = 34²

Simplifying and solving for h.

h² = 34² - 24²

h² = 676 - 576

h² = 100

h = 10

Therefore,

The height of the building is 10 meters.

Learn more about the Pythagorean theorem here:

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Answer:

A correlation coeff close to +1 would have a positive slope, and all dots representing the data set would be quite close to the regression line.  

Correlation is a measure of association between two variables. IF there is a perfect linear association then correlation would be nearer to 1.  

Correlation always lies between -1 and +1.

If between-1 and 0 we say there is a negative correlation.

If nearer to 1 than to 0 then we say strong correlation

Here given correlation is 0.95 i.e. positive and have almost perfect linear relation.

Hence we see that Graph C shows almost linear relationship with slope positive

So option C is answer

Answer:

2.1275 is 2.12747677748 rounded to the nearest ten-thousandth.

Step-by-step explanation:

Since the hundred-thousandth place is 5 or above, we would round the ten-thousandths place up. THis makes the number 2.1275.

Answer:

(x-8)^2+(y-16)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2+(y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-8)^2+(y-16)^2 = 2^2

(x-8)^2+(y-16)^2 = 4

Answer:

Answer From Gauth Math

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

i can help you in any time

Answer:

Step-by-step explanation:

I'm not sure but i think your right