Choose the equation that satisfies the data in the table

Answer:

cake 90

Step-by-step explanation:

8×5×2=90

length ×width ×height

The time that the  height of 80 feet occur on the interval 0 is 4.662 seconds.

Given:

50 cos (π/15(x-10))+52

Height=80 feet

Time= x second

Hence:

height (h)= 50 cos [pie(x - 10 )/15 ] + 52

80 = 50 cos [pie( x - 10 )/15 ]+ 52

Collect like terms

80 - 52 = 50 cos [ pie( x - 10 )/15 ]

28 = 50 cos [ pie( x - 10 )/15 ]

cos [pie( x - 10 )/15 ] = 28/50

cos [ pie( x - 10 )/15 ] =56

cos [pie( x - 10 )/15 ]= cos ( 56 )

cos [ pie( x - 10 )/15 )]= cos ( 0.3111 pie )

Hence:

pie( x - 10 )/15 = 0.3111

( x - 10 )/15 = 0.3111

x - 10 = 15 × 0.3111

x - 10 = 4.662

x = 10 + 4.662

x = 14.662 seconds

Therefore the correct option is C.

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Answer:

1. 4-2=2

2.2 10/21

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

In math, volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object.

Answer:

256π cm³

Step-by-step explanation:

πr²·h=Volume

π·(4)²·16=π·16·16=256π cm³

Answer:

the height is 11 units the base is 12 units and the area is (i think) 84

Answer:

-.4685

Step-by-step explanation:

[tex]x^y=z\\y=log_zy\\10^{x+2}=34\\x+2=log_{10}34\\x+2=log34\\x+2=1.531478917\\x=-.468521083[/tex]

Answer:

233.28

Step-by-step explanation:

I'm assuming that you are trying to find the volume of a rectangular prism.

If so, [tex]5.4*7.2*6 = 233.28.[/tex]

Therefore, the volume of the rectangular prism is 233.28; I'm not sure of the unit.

Answer: -3

Step-by-step explanation:

Given

Equations of the lines are

[tex]y=-x-4\\3y=cx-18[/tex]

For the system of linear equation [tex]a_1x+b_1y=c_1,a_2x+b_2y=c_2[/tex] has no solution if

[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}[/tex]

Rewrite the equations

[tex]x+y=-4,\ cx-3y=18[/tex]

Insert the values for the no solution condition

[tex]\Rightarrow \dfrac{1}{c}=\dfrac{1}{-3}\\\\\Rightarrow c=-3[/tex]

Therefore, for c=-3, the system of linear equation ha no solution.

Answer:

[tex]an=2n+4[/tex]

Step-by-step explanation:

Answer:Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

3.5×10^−12

Step-by-step explanation:

in simple terms 3.5×10^−12 or 3.5 times 10 to the power of -12

Answer:

X=6

Step-by-step explanation:

As you know x then you can use tan to do

[tex] \tan( \binom{5}{6} ) = o \\ [/tex]

Then you will get the answer of 39°48'

Answer:

200.06

Step-by-step explanation:

Area= πr2

Divide 16/2 to get radius

A= 3.14 x 8 x 8

A= 3.14 x 64

A= 200.06

The minimum amount of extra cardboard needed to construct a new box is : 84in².

First step

Surface area=2(16) (5) in²+ 2(20in) (5in)  + 2(16in) (20in)

Surface area=1000in²

Second step

Surface area if the length increase by 2 inches

Surface area=2(16) (5) + 2(20+2) (5in)  + 2(16in) (20+2)

Surface area=1084in²

Third step

Surface area=1084in²-1000in²

Surface area=84in²

Therefore the minimum amount of extra cardboard needed to construct a new box is : 84in².

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Answer:

The area of the shape is 122.30 cm^2

Step-by-step explanation:

To calculate the surface area, we identify the side shapes

We have this as;

a rectangle that measures 11 cm by 3 cm, a rectangle that measures 3 cm by 6 cm, a rectangle that measures 8 cm by 3 cm, 2 triangles ( base and top) that has a height of 4.3 cm and a base of 11 cm

The area of the rectangles is simply the product of the side lengths

The area of the triangles is the product of the base and the height divided by 2; but since we have 2 exact triangles, we can simply multiply the base and the height to serve as the area of both

Thus, we have the area of the shape as follows;

(11 * 3) + (3 * 6) + (8 * 3) + (4.3 * 11)

= 33 + 18 * 24 + 47.3

= 122.30 cm^2

Answer:

[tex]Mean = \$15[/tex]

[tex]Standard\ Deviation = \$53.85[/tex]

Step-by-step explanation:

Given

See attachment for probability distribution

Required

Determine the mean and the standard deviation

The mean of the distribution is:

[tex]Mean = E(x)[/tex]

and

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]Mean = \$500 * 0.01 + \$100 * 0.05 + \$25 * 0.20 + \$0 * 0.74[/tex]

[tex]Mean = \$5 + \$5 + \$5 + \$0[/tex]

[tex]Mean = \$15[/tex]

So:

[tex]E(x) = 15.00[/tex]

The standard deviation of the distribution is:

[tex]S = \sqrt{Var(x)}[/tex]

Where:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 500^2 * 0.01 + 100^2 * 0.05 + 25^2 * 0.20 +0^2 * 0.74[/tex]

[tex]E(x^2) = 2500 + 500 + 125 +0[/tex]

[tex]E(x^2) = 3125[/tex]

So:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where

[tex]E(x^2) = 3125[/tex]

[tex]E(x) = 15.00[/tex]

[tex]Var(x) = 3125 - 15^2[/tex]

[tex]Var(x) = 3125 - 225[/tex]

[tex]Var(x) = 2900[/tex]

Recall that:

[tex]S =\sqrt{Var(x)[/tex]

[tex]S =\sqrt{2900[/tex]

[tex]S =53.85[/tex]

Answer:

12        4          (12, 4)

18        6          (18, 6)

Step-by-step explanation:

On coordinate plane, the "add 6" column values are x-axis values and "add 2" column values are y-axis values.

Answer: 15

Step-by-step explanation:

Factors:

75: 1, 3, 5, 15, 25,

15: 1, 3, 5, 15

Write out all the factors of each number and circle the highest factor that both numbers have

Answer:

x =4 and y =1

Step-by-step explanation:

Triangle ADB is an equilateral triangle that means the side a 3 unit each

so,

y + 2 = 3

y = 1

Triangle DBC is an isosceles triangle that means two legs are equal

So,

y + 2 = x -1

we already know that y+2 = 3

So,

3 = x -1

4 = x

Answer:

85 hours

Step-by-step explanation:

Number of hours per day = 13 hours

Number of days = 6

Number of hours worked for 6 days = 6 days × 13 hours

= 78 hours

then he worked 7 hours

Total Number of hours worked = Number of hours worked for 6 days + 7 hours

= 78 hours + 7 hours

= 85 hours

Total Number of hours worked = 85 hours

Answer:

B and F are non-statistical questions

Step-by-step explanation:

B is asking how many years until you are 16; this is not statistical because it just a fact. F is pretty much the same because it's just asking a subjective fact-like question.

Statistical questions ask for a collection of varying data. If there is only one data point, it is non-statistical.

Answer:

It is C.

III is saying that the two functions are inverse functions. If two functions, f(x) and g(x) are inverse, then f(g(x)) = x and g(f(x)) = x. Therefore, we see that if III is true, then I and II should also be true. Now, all we have to prove is that f(x) and g(x) are inverse functions. As we said before, if two functions are inverse, then f(g(x)) = x and g(f(x)) = x.

f(g(x)) = 3([tex]\sqrt[3]{\frac{x-2}{3} }[/tex])^3 + 2

f(g(x)) = 3[(x-2)/3]+2

f(g(x)) = x-2 + 2

f(g(x)) = x

Therefore, we have proved that f(g(x)) = x, and so f(x) and g(x) are inverse functions, and so all of I, II, and III are true. Thus, the answer is C.

fyi, we didn't have to do g(f(x)) because if f(g(x)) = x, then so will g(f(x)).

Answer:

4 and 3/4 inches less for April

and 1 and  1/2 inches  less for March

Step-by-step explanation:

Answer:

take another pic I can't see because of the glare

Answer:a I think

Step-by-step explanation:

Answer:

B.) 90

Step-by-step explanation:

Number line graph with closed circle on 90 and shading to the right. It shows that 90 should be greater or more. So its B.

I hope this helped! I also took the test and got it correct! :)

Answer:

80000

Step-by-step explanation:

Answer:

If its set up like

1 2

3 4

5 6

the answer is 1,2,4,6

Step-by-step explanation:

i hope my math on desmos was right xD

The equations of ellipses[tex]2x^{2} +8y^{2} -12x+16y-174=0[/tex], [tex]4x^{2} +y^{2} +16x+4y+4=0[/tex],[tex]3x^{2}+12y^{2} +18x-24y-69=0[/tex] and [tex]x^{2} +9y^{2} -2x+18y-71=0[/tex] having the major axis lengths are twice their minor axis length.

Equations of ellipse

[tex]\frac{(x-h)^{2} }{a^{2} } +\frac{(y-k)^{2} }{b^{2} } =1[/tex]         (for horizontal major axis ,a>b)

[tex]\frac{(x-h)^{2} }{b^{2} } +\frac{(y-k)^{2} }{b^{2} }=1[/tex]           ( for vertical major axis, b>a))

Where, (h, k) is the center of ellipse.

The major axis of an ellipse is its longest diameter(a line that runs through the center and both foci, with ends at the two most widely separated points  on perimeter).

length of major axis = 2a       (where a is the length of semi major axis)

The minor axis of an ellipse is the line that contains the shorter of the two line segments about which the ellipse is symmetrical.

length of minor axis = 2b               (where b is the length of semi minor axis)

According to the given question

we have, the equations  of ellipses

A) [tex](4x^{2} +32x)+(25y^{2} -250y)+589=0[/tex]

[tex]4(x^{2} +8x)+25(y^{2} -10y)+589=0[/tex]

[tex]4(x^{2} +8x+b^{2} )-4b^{2} +25(y^{2} -10y+b^{2} )-25b^{2} +589=0[/tex]

[tex]4(x^{2} +8x+4^{2})-4(4^{2})+25(y^{2} -10y+b^{2} )-25(5^{2} ) +589=0[/tex]

[tex]4(x+4)^{2}+25((y-5)^{2} )-100=0[/tex]

[tex]4(x+4)^{2} +25(y-5)^{2} =100[/tex]

dividing both the sides by 100

[tex]4\frac{(x+4)^{2} }{100} +25\frac{(y-5)^{2} }{100} =1[/tex]

[tex]\frac{(x+4)^{2} }{25} +\frac{(y-5)^{2} }{4} =1[/tex]

[tex]\frac{(x+4)^{2} }{5^{2} } +\frac{((y-5)^{2} }{2^{2} }=1[/tex]

here, h=-4 and k=5

major axis =2a=2×5=10

minor axis=2b=2×2=4

⇒ the length of major axis is not twice the length of minor axis.

Similarly, we will do for the other equations

B).

[tex]2x^{2} +8y^{2} -12x+16y-174=0\\\frac{(x-3)^{2} }{10^{2} } +\frac{(y+1)^{2} }{5^{2} } =1[/tex]

here, h=3 and k=-1

major axis:2a=2×10=20

minor axis:2b=2×5=10

⇒ length of major axis is twice the length of minor axis.

C).

[tex]4x^{2} +y^{2} +16x+4y+4=0[/tex]

[tex]\frac{(x+2)^{2} }{2^{2} } +\frac{(y+2)^{2} }{4^{2} } =1[/tex]

here, h=-2 and k= -2

major axis: 2b=2×4=8

minor axis: 2a= 2×2=4

⇒ the length of the major axis is twice of the length of minor axis.

D).

[tex]x^{2} +4y^{2} +6x-8y-23=0[/tex]

[tex]\frac{(x+3)^{2} }{6^{2} } +\frac{(y-1)^{2} }{3^{2} } =1[/tex]

here, h=-3 and k=1

major axis: 2a=2×6=12

minor axis: 2b= 2×3=6

⇒ the length of major axis is twice of the length of minor axis.

E).

[tex]16x^{2} +y^{2} -64x+8y+16=0[/tex]

⇒[tex]\frac{(x-2)^{2} }{2^{2} } +\frac{(y+4)^{2} }{2^{2}} =1[/tex]

here, h=2 and k=-4

major axis: 2a=  4

minor axis :2b=4

⇒ the length of major axis is not the twice of minor axis.

F)

[tex]x^{2} +9y^{2} -2x+18y-71=0[/tex]

⇒[tex]\frac{(x-1)^{2} }{9^{2} } + \frac{(y+1)^{2} }{3^{2} } =1[/tex]

here, h=1,  and k=-1

major axis: 2a= 18

minor axis: 2b = 9

⇒ the length of major axis is twice to the length of minor axis.

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