Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$

By evaluating the piecewise function, we get:

g(-2) = 0.

g(4) = 4.

A piecewise function is a function that behaves differently in different parts of its domain.

Here, we first want to get g(-2). x = -2 belongs to the second domain, then we use that part:

g(-2) = 0.

For x = 4, it belongs to the third domain, then we have:

g(4) = 4.

If you want to learn more about piecewise functions:

https://brainly.com/question/3628123

#SPJ1

The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49

The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have

The cubic equation will be

e³ˣ + eˣ - 6 = 0

Let eˣ = u, then the equation will be

u³ + u - 6 = 0

Then the root of the equation is calculated by the calculator, then we have

u = 1.634, -0.817, -0.817

eˣ = 1.634, -0.817, -0.817

Take log on both sides, then we have

x = ln 1.634, ln(-0.817), ln(-0.817)

x = 0.49, not defined, not defined

Then the value of x will be 0.49.

More about the cubic equation link is given below.

https://brainly.com/question/13730904

#SPJ1

Answer:

36

Step-by-step explanation:

Question:

[tex] \bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solution:

Here, we need to use PEMDAS rule, where:

There's a rule as well, the sum given is need to solved from the left, whichever sign is there.

Solved:

[tex]\bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solve for parentheses first:

[tex] = 5 \times 7 + 5 - 4[/tex]

Then multiplication of course:

[tex] = 35 + 5 - 4[/tex]

Then addition:

[tex] = 4 0 - 4[/tex]

[tex] =36[/tex]

Hence, the answer is 36.

Answer: 453.592 grams

Step-by-step explanation:

I searched it up online. But if you're going to use this to calculate. Use 454 grams.

Answer:

453.592 rounded would be 454* grams witch is equal to 1 pound

Step-by-step explanation:

1 pound is equivalent to __453.592 or just say 454*__ grams.

Had to fix that hehehe

Hope This Helped

Answer:

Can't see the problem. Send a picture of it.

The equations of the graphed line and function can be written as:

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

y - 1 = 0.5(x + 2)

Equation of a graphed line can be expressed in:

Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or

Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.

Find the slope (m) of the line:

Slope (m) = change in y / change in x = 1/2 = 0.5

y-intercept (b) = 2

To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:

f(x) = 1/2x + 2.

Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):

y - 3 = 1/2(x - 2)

Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):

y - 1 = 0.5(x - (-2))

y - 1 = 0.5(x + 2)

Learn more about the equation of a graphed line on:

https://brainly.com/question/11490660

#SPJ1

Answer:

Answer is $2,637.38

Step-by-step explanation:

The ratio of the area of sector abc to the area of sector dbe is 4/3

For sector abc, we have:

Angle = x

Radius  = 2r

For sector dbe, we have:

Angle = 3x

Radius = r

The area of a sector is:

[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]

So, we have:

[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]

Evaluate

[tex]ABC =\frac{x* \pi r^2}{90}[/tex]

For DBE, we have:

[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]

Evaluate

[tex]DBE =\frac{x}{120}* \pi r^2[/tex]

The ratio of both areas is:

[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]

Cancel out the common factors

[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]

Express as fraction

[tex]Ratio = \frac{120}{90}[/tex]

Divide

[tex]Ratio = \frac{4}{3}[/tex]

Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3

Read more about sector areas at:

https://brainly.com/question/1582027

#SPJ4

4/3

its the answer edmentum

Step-by-step explanation:

y + 1 = 2(x + 5) = 2x + 10

y - 9 = 2x

2x - y = -9

Answer:

37

20

C

a

→

37

19

K

+

0

+

1

e

This equation shows us the parent atom, which is calcium-37. The mass number is written above the atomic number for the atom. The arrow indicates the decay process with the products to the right of the arrow. The products are an atom of potassium-37 and a positron, which is similar to an electron but it carries a charge of +1 instead of a charge of -1. We can see that the transition of a proton to a neutron in positron decay decreases the atomic number of the atom from 20 to 19, but the mass number of 37 remains the same.

Step-by-step explanation:

Answer:

37

20

C

a

→

37

19

K

+

0

+

1

e

Step-by-step explanation:

Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the rule is given by:

(x, y) -> (x+4, y-2).

Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:

2 + 4 = 6.

The x-coordinate of S' is given by 6.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]

Answer:

see the attachment photo!

Answer: pi/4 and -1

Step-by-step explanation:

Answer:

do u still need help with this

AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.

1. P(A and 1) = 1/4 x 1/6 = 1/24

2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12

3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12

4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12

5. P(C and 3) = 1/4 x 1/6 = 1/24

6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6

7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4

8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8

9. P(a vowel and a 5) = 1/4 x 0/6 = 0

10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8

11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12

Experimental probability is based on something that has already happened, or data that has already been collected.

12. P(1) = 3/30 = 1/10

13. P(2) = 8/30 = 4/15

14. P(3) = 7/30

15. P(4) = 5/30 = 1/6

16. P(5) = 3/30 = 1/10

17. P(6) = 4/30 = 2/15

Hope this helps!

Answer: (0, 1), (-1, -3)

Given two equation's:

Solve them simultaneously:

[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]

[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]

[tex]\sf 6x^2 + 6x = 0[/tex]

[tex]\sf 6x(x + 1) = 0[/tex]

[tex]\sf 6x = 0, \ x + 1 = 0[/tex]

[tex]\sf x = 0, \ x = -1[/tex]

(a) When x = 0,     y = −4(0)² + 1 = 1

(b) When x = -1,    y = -4(-1)² + 1 = -3

Solution: (x, y) → (0, 1), (-1, -3)

Answer:

System of equations

[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]

To solve the given system of equations, use the substitution method:

[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]

Therefore the x-values of the solutions are:

        [tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]

Substitute the found values of x into the second equation to find the y-values:

[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]

Therefore, the solutions of the system of equations are:

(-1, -3) and (0, 1)

Answer:

Step-by-step explanation:

Formula

The sin(A) =  opposite / hypotenuse

Givens

Opposite = CB = 11

Hypotenuse = AB = 61

Solution

Sin(A) = 11/61

Sin(A) = 0.1803

Answer

Sin(A) = 11/61

Sin(A) = 0.1803

Answer:

(2+3)+4 = 2+(3+4) this is an example of associative property

Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

Answer:

$50 interest

Step-by-step explanation:

Simple interest formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for I:

⇒ I = 500 · 0.02 · 5

⇒ I = 50

Therefore, Frank will earn $50 interest in 5 years.

Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]

Answer:

see attached

Step-by-step explanation:

Morning:

12, 19, 19, 21, 23, 25, 27, 31, 36, 39

Min value: 12

Lower quartile (Q1): 19

Median (Q2): 24

Upper Quartile (Q3): 31

Max value: 39

Afternoon:

8, 8, 11, 15, 16, 27, 34, 39, 43, 51

Min value: 8

Lower quartile (Q1): 11

Median (Q2): 21.5

Upper Quartile (Q3): 39

Max value: 51

Answer:

7.  AM IQR: 12   PM: IQR: 28  8. see below in explanation

Step-by-step explanation:

7. 31-19=12

    39-11= 28

You subtract Q1 from Q3 to get the IQR.

8. I believe the morning group of dogs would be easier to walk as one group because the group has a closer range of weights (12-39) compared to the afternoon group of (8-51). Walking a large group of dogs with similar weights would be easier than walking a group of very small and very large dogs at the same time because their pace of walking would be so different.

Outlet A sold the greatest number of copies of album x in July and August

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A  = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A  = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

Read more about two-way tables at:

https://brainly.com/question/15940356

#SPJ1

Answer:

Outlet D

Step-by-step explanation:

they sold 28 of album x

outlet a only sold 26

The true statement is the cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

In store 1, the cost of 1 pound of steak is $6.75.

Cost of 1 pound of steak in store 2 is 15 /2 = $7.50

Difference in the cost : $7.50 - $6.75 = $0.75

Here is the complete question:

The equation y = 6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights of steak at grocery store 2.

Cost of Steak at Grocery Store 2

Weight (pounds) Cost

2..........................$15.00

3..........................$22.50

5......................... $37.50

9......................... $67.50

Which statement is true?

answer choices

The cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.75 more per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.50 less per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.50 more per pound than at grocery store 2. R

To learn more about division, please check: https://brainly.com/question/194007

#SPJ1

After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have:

If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.

We know the exponential decay can be given as:

D = a(1 - r)ⁿ

a is the starting value and n is the number of hours.

D = 75(1 - 0.20)⁶

D = 19.66 milligrams

Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

Learn more about the exponential decay here:

brainly.com/question/14355665

#SPJ1

Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.

Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.

In other words, 5 + (-3) = 5 - 3 = 2