is the number -71.52 rational?

Answer:

-62.5008

Step-by-step explanation:

Find the pattern first: -75/15 = -5

Find the first 7 terms: -3/-5, 3/25, -3/125, 3/625

Add: -62.5008

Answer:

  -62.5008

Step-by-step explanation:

The terms form a geometric sequence with first term -75 and common ratio -1/5. The sum of n terms of such a sequence is...

  Sn = a1(1 -r^n)/(1 -r)

For the values of a1, r, and n, this sum is ...

  S7 = -75(1 -(-1/5)^7)/(1 -(-1/5)) = -75(1 +1/78125)/(1 +1/5)

  = -75(13021/15625) = -62 313/625

  = -62.5008

The sum of the first 7 terms of the sequence is -62.5008.

Answer:

1/10

Step-by-step explanation:

So first we need to find the probability of the cards, there is 5 cards and one card needs to be chosen, so the probability is 1/5

Then we need to find the probability of the dice, there is 3 even numbers in 1,2,3,4,5,and 6, so the probablity is 3/6 which is also equal to 1/2

Finaly we need to multiply 1/5 with 1/2, which is 1/10

Answer:

The vertex of the function is at (1,-25)

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one.

Part of the graph of the function f(x) = (x + 4)(x-6) is shown  below.

Which statements about the function are true? Select two

options.

The vertex of the function is at (1,-25).

The vertex of the function is at (1,-24).

The graph is increasing only on the interval -4< x < 6.

The graph is positive only on one interval, where x <-4.

The graph is negative on the entire interval  

My answer:

Given the factored form of the function:

f(x) = (x + 4)(x-6)

<=> f(x) = [tex]x^{2} - 2x -24[/tex]

We will convert to vertex form

<=> f(x) = ([tex]x^{2} - 2x +1[/tex]) - 25

<=> f(x) = [tex](x-1)^{2} -25[/tex]

=> the vertex of the function is: (1,-25)

We choose: a. The vertex of the function is at (1,-25)

Let analyse other possible answers:

c. The graph is increasing only on the interval -4< x < 6.

Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.

So the graph is increasing in the domain (1, +∞)

=> C is wrong

d. The graph is positive only on one interval, where x <-4

Wrong, The graph is positive only on one interval, where x > 6

e. The graph is negative on the entire interval

Wrong, The graph is negative only on one interval, where -4< x < 6.

Answer:

[tex]d = \frac{t - 7c}{ - 2} [/tex]

Hope this helps at all. :)

To solve for d in T = 7c - 2d, isolate the variable d by moving the term with d to the other side of the equation and simplifying.

To solve for d in the equation T = 7c - 2d, we need to isolate the variable d. First, we'll start by moving the term with d to the other side of the equation.

Step 1: Add 2d to both sides of the equation.

T + 2d = 7c

Step 2: Now, we'll isolate the variable d by subtracting T from both sides of the equation.

2d = 7c - T

Step 3: Finally, divide both sides of the equation by 2 to solve for d.

d = (7c - T)/2

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Answer:

7.68 s

Step-by-step explanation:

The vertical motion formula is:

[tex] h_{t} = h_{0} + v_{0}t - \frac{gt^{2}}{2} [/tex]

Where:

h(t): is the final height = 0

h(0): is the height of the cliff = 104 foot

v(0): is the initial velocity = 110 ft/s

g: is the gravity = 9.8 m/s² = 32.15 ft/s²

Hence, from the vertical motion formula we can find the time that will take the rocket to hit the ground:

[tex] 0 = 104 + 110*t - \frac{32.15t^{2}}{2} [/tex]

[tex] 0 = 104 + t(110 - 16.08t) [/tex]

We have two solutions:

t₁= -0.84 s

t₂ = 7.68 s

We will take the positive value, thus the time that will take the rocket to hit the ground is 7.68 s.

I hope it helps you!

Answer:

A

Step-by-step explanation:

option A is correct,  2a³/b⁴ is expanded to log2+3loga-4logb

An expression is combination of variables, numbers and operators.

The given expression is 2a³/b⁴

We have to expand this by using logarithms.

logab=loga +log b

log(a/b)=loga-logb

log(2a³)/log(b⁴)

log2+loga³ - log(b⁴)

Another property of logarithm

logaˣ=xloga

log2+3loga-4logb

Hence, option A is correct,  2a³/b⁴ is log2+3loga-4logb

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Answer:

1120 grams

Step-by-step explanation:

The amount of sea water is directly proportional to the amount of salt in the water.

Let the amount of sea water be W and the amount of salt be S.

This means that:

W α S

=> W = kS

where k = constant of proportionality

2 liters of sea water contain 70 grams of salt Therefore:

2 = k * 70

k = 2 / 70 = 1/35

Therefore, for 32 liters of sea water:

32 = 1/35 * S

S = 35 * 32

S = 1120 grams

There are 1120 grams of salt in 32 liters of water.

Answer:

47.16 Square centimeters

Step-by-step explanation:

Width=7.2cm

Length =19cm

Height =32cm

Surface Area=2(LW+LH+WH)

=2(19*7.2+19*32+7.2*32)

Surface Area [tex]=1950.4 cm^2[/tex]

When the height is increased by 0.9cm

Height =32.9cm

Surface Area=2(LW+LH+WH)

=2(19*7.2+19*32.9+7.2*32.9)

Surface Area [tex]=1997.56 cm^2[/tex]

Difference in Surface Area=1997.56-1950.4

=47.16 Square centimeters

An alternative way is to calculate the surface area dealing with the height only using the height difference,

Difference=2(LH+WH)

=2(19*0.9+7.2*0.9)

=47.16 Square centimeters

Answer:

[tex]y = 9[/tex]

Step-by-step explanation:

[tex]28 + 7y = 91 \\ 7y = 91 - 28 \\ 7y = 63 \\ \frac{7y}{7} = \frac{63}{7} \\ y = 9[/tex]

Answer:

Y=9

Step-by-step explanation:

28 + 7y =91

first subtract 28 from both sides

28-28+7y=91-28

7y= 63

then divide both sides by 7

7y/7=63/7

y=9

ANSWER CHECK

to see if the answer is correct substitute the answer you got for the variable

y=9

28 + 7(9)

multiply 7 and 9

7(9)=63

63+28= 91

Answer:

18/m - 3

Step-by-step explanation:

To simplify the expression 5.2 + 3.6x - 8 + x, combine like terms to get -2.8 + 4.6x, which is the final simplified expression.

The student's question involves simplifying the expression 5.2 + 3.6x – 8 + x. To simplify the given algebraic expression, combine like terms. Like terms in this expression are the constant terms (5.2 and -8) and the variable terms (3.6x and x).

First, add the constant terms together:

5.2 - 8 = -2.8

Then, combine the variable terms:

3.6x + x = (3.6 + 1)x = 4.6x

Now, put the constants and variable terms together to get the simplified expression:

-2.8 + 4.6x

To check if the simplified expression is reasonable, ensure that all like terms have been correctly combined. There is no further simplification possible, so this is the final answer.

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Answer:

5,5

Step-by-step explanation:

(5, 5)

This is very correctamundo

Answer:

[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]

And replacing we got:

[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]

And the probability required for this case is 0.4375

Step-by-step explanation:

For this case we define the following events:

H = represent that the student is honorable

P= represent that the student have a part time job

And we have the following probabilities:

[tex] P(H) = 0.42 , P(P) = 0.64, P(H \cap P) =0.28[/tex]

And we want to find this probability:

[tex] P(H|P)[/tex]

And we can use the following probability:

[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]

And replacing we got:

[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]

And the probability required for this case is 0.4375

Answer:

Step-by-step explanation:

[tex]Width=\frac{Area}{length}\\\\=\frac{36}{9}\\\\[/tex]

= 4 inches

Answer:

9×W=36 or 36÷9=W

Step-by-step explanation:

to find the area of a figure you multiply L×W in this situation you only have length. soo find what times 9 = 36 or 36÷9 to find Width

Answer:

Faith means to believe in something you cannot see.

Step-by-step explanation:

An example can be oxygen. To a naked eye, you cannot see oxygen, yet you "believe" that it is there, or you have faith that there is oxygen around you to sustain you.

This is what faith is, the belief of something that you cannot see with the naked eye.

~

Answer:

Faith is a trust or confidence in a person, object, or concept.

Example:

"The dog remained faithful to his owner."

"They lost faith when he lied to them."

Answer:

The answer is this.

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

Hope this helps ya.

☆CHEERS!☆

Answer:

(5,0) and (-1,0)

Step-by-step explanation:

Answer:

x = 8 inches length

Step-by-step explanation:

Dimension of box:

12 inches  by 2 inches by length x

with total surface area = 272 square inches,

There are 6 faces.

Area =  2 *(12 * 2) + 2 *(2*x) + 2 *(12*x)

Area = 272 sq. in.  = 48 + 4x + 24x

272 = 48 + 28x

272 - 48 = 28x

224 = 28x

x = 8 inches

To find the length of the box, use the surface area formula of a rectangular prism and solve for the length. The length of the box is 59 inches.

To find the length of the box, we need to calculate the dimensions of the cereal box. The surface area of a rectangular prism is given by the formula: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the box. From the given information, we have:

12(2) + 12(1) + 2(2)x = 272

Simplifying the equation gives us: 24 + 12 + 4x = 272

Combining like terms, we have 4x + 36 = 272. Subtracting 36 from both sides gives us 4x = 236. Finally, dividing by 4 gives us x = 59.

Therefore, the length of the box is 59 inches.

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Answer:

First one:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

3 and one-fifth + n = 9

3⅕ + n = 9

3⅕ + n - 3⅕ = 9 - 3⅕

n = 5⅘

Answer:

first choice

Step-by-step explanation:

give brainileast to the other guy plas

Answer:

The circumference of a circle is not the same as the area of the circle because the circumference represents the distance around the circle while the area represents the amount of space within the circle. Hope this helps.

Answer:

No

Step-by-step explanation:

The circumference of a circle is the distance around the outside of the circle. It is similar to the perimeter of other shapes such as squares.

Hope this helps! :)

Answer:

True

Step-by-step explanation:

Answer:

100 degrees

Step-by-step explanation:

Arc QM = Arc QN = 130°

Arc MN = 360 - Arc QM - Arc QN

= 360 - 2(130)

= 360 - 260

= 100°

Answer:

The absolute value of a number is a distance /2/=2

Step-by-step explanation:

The absolute value of the absolute expression |2| will be 2.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute expression is given below.

⇒ |2|

The value will be always positive when the value inside the mode is taken out. Then we have

⇒ |2|

⇒ 2

The absolute value of the absolute expression |2| will be 2.

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A "triangle" with the angles 0, 90, and 90 degrees cannot be considered a triangle since the two 90 degree angles make a right angle, and 0 degrees would mean a flat line. Rather it would resemble something like a straight U that is stretched sideways.

Final answer:

A figure with angles of 0, 90, and 90 degrees cannot be considered a triangle because the angles must sum to 180 degrees and each angle must be greater than 0 degrees and less than 180 degrees to form a three-sided figure.

Explanation:

A triangle is defined as a three sided figure lying on a plane, with three angles that add up to 180 degrees. In the case of the angles provided (0, 90, and 90), they do not add up to 180 degrees; instead, they sum up to 180 degrees if you exclude the 0-degree angle, which cannot be a valid angle for a triangle since every angle in a triangle must be greater than 0 degrees and less than 180 degrees. Therefore, a figure with angles of 0, 90, and 90 degrees cannot be considered a triangle.

In addition, the shape with two 90-degree angles would be a straight line, which does not meet the criteria of a triangle having three sides. An example of a valid right-angled triangle is one having angles of 90, 45, and 45 degrees, which correctly sum up to 180 degrees and form a closed three-sided figure.

Answer:

-8

Step-by-step explanation:

x less than or equals to -8

Answer:

If you are moving up the line toward the 0, the answer would be more than

If you are moving down the line, -72 would be more than -64.

Step-by-step explanation:

8 times negative 8 is -64     --- I think

Answer:

27218

Step-by-step explanation:

y= 17000 (1.04) ^12

y=27217.54772

y= 27218

If a town has a population of 17000. The population after 12 years, to the nearest whole number is 27,218.

Using this formula

A=P(1+r/100)^n

Let plug in the formula

A= 17000 (1+.04) ^12

A= 17000 (1.04) ^12

A=17000×1.601032

A=27217.54

A=27218 (Approximately)

Therefore the population after 12 years, to the nearest whole number is 27,218.

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Answer:

80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].

Step-by-step explanation:

We are given that James takes a random sample of 42 homes form the Austin MLS (that's where Realtors go for information) and finds that 29 of them are listed as "eclectic" style.

Firstly, the pivotal quantity for 80% confidence interval for the population proportion is given by;

                              P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of homes that are "eclectic" = [tex]\frac{29}{42}[/tex] = 0.69

            n = sample of homes = 42

            [tex]\mu[/tex] = population proportion of homes that are "eclectic"

Here for constructing 80% confidence interval we have used One-sample z proportion statistics.

So, 80% confidence interval for the population proportion, p is ;

P(-1.282 < N(0,1) < 1.282) = 0.80  {As the critical value of z at 10% level

                                                     of significance are -1.282 & 1.282}  

P(-1.282 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.282) = 0.80

P( [tex]-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

P( [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

80% confidence interval for p = [ [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex],[tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

= [ [tex]0.69-1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] , [tex]0.69+1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] ]

= [0.59 , 0.78]

Therefore, 80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].