What is the equation for the line of best fit on the scatter plot below?

The annual interest paid on the account is $75

The formula for determining annual interest is given as;

Interest = PRT/100

where;

Substitute the values

Annual Interest = 1000 × 7. 5 × 1/ 100

Annual interest = 7500/ 100

Annual interest = $75

Thus, the annual interest paid on the account is $75

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Answer:

C. 206 unit^2.

Step-by-step explanation:

Area = 2*11*5 + 2*11*3 + 2*3*5

         = 110 + 66 + 30

         =  206.

Answer:

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Step-by-step explanation:

Tossing a coin has two possible outcomes, heads (H) and tails (T).

Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.

Table:

First spin                   H     H     H     H     H    T     T     T     T     T

Second spin              1      2      3     4      5     1     2     3     4     5

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.

Y assume we have an exponential equation of the form:

y = a*b^x + c

In this case, a is what we know as the "initial value" of the exponential.

Notice that when we evaluate in x = 0, we get:

y = a*b^0 + c

y = a + c

So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.

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Answer:

7/14, so 50%

Step-by-step explanation:

Answer:

Y = 2+- square root of 6

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets solve ~

Let's calculate its discriminant ~

[tex]\qquad \sf  \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16 - ( - 8)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]

So, by quadratic formula :

[tex]\qquad \sf  \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]

Answer:

110 degrees

Step-by-step explanation:

to find the angle x, we need to use the formula to find the 50 degree angle:

(y - x) / 2 = 50

y is 210

(210 - x) /2 = 50

210-x = 100

x = 110 degrees

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Answer:

Step-by-step explanation:

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]

and z = r

A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.

Given:

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

By applying two more row operations, we get

[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]

simplifying the above matrix, we get

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]

[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and

z = r

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The correct option B.

The value of the zeros of function g is -6 and 7

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

The factors are  (x − 7) and (x + 6)

On simplifying the we get:

x²+ 6x -7x -42 = 0

x² - x - 42 = 0

The factorizing these equation we get.

So the zeros are -6 and 7 , so option b is correct.

[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]

[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]

[tex]x_1,_2[/tex] = ((1) ± 13)/2.1

[tex]x_1[/tex]    = (1+13)/2.1

[tex]x_2[/tex]     = (1 - 13)/2.1

[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6

The Zeros of the function are: (7 , -6)

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Answer:

x=1990

Step-by-step explanation:

x+10=2000

x=2000-10

x=1990

Answer:

therefore x = 1990

Step-by-step explanation:

x+10 = 2000

= x = 2000-10

= x = 1990

Answer:

b=67.5°

Step-by-step explanation:

hope it helps!!!

Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.

The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

A line segment that divides an angle into two equal parts is referred to as an angle bisector.

From the proof given, we know that;

m∠DEK = 2(m∠DEF)

m∠DEK = 2(44) = 88°

With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.

Then, KF = 1/2(DK) = 1/2(16) = 8.

The complete proof is show in the image attached below.

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Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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Answer:

t ≥ 36

Step-by-step explanation:

took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.

The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

We know that t is the time,  in minutes, since Marcel plugged in the phone and the tablet.

For phone:-

Initial battery charge = 13%.

Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.

Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.

For tablet:-

Initial battery charge = 25%.

Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.

Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.

We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.

Since the phone is required to have at least as much battery charge as the tablet, we can show this as:

The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,

or, 13% + t(2/3)% ≥ 25% + t(1/3)%,

or, t(2/3)% - t(1/3)% ≥ 25% - 13%,

or, t(1/3)% ≥ 12%,

or, t ≥ 12%/(1/3)%,

or, t ≥ 36.

Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]

we need to find -4 h(9) :

[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]

[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]

[tex]\qquad❖ \: \sf \:4[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:

The smallest 3-digit base-11 number is 100

When converted to base 10, the equivalent number is 121

The largest 3-digit base-9 number is 888

When converted to base 10, the equivalent number is 728

So, the total number of possibilities is:

Possibilities = 728 - 121 + 1

Possibilities = 608

The count of base 10 3-digit numbers is

Count = 999 - 100 + 1

Count = 900

The required probability is:

P = 608/900

Evaluate

P = 0.6753

Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

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Complete question

A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals

A one-tailed test's p-value is half that of a two-tailed test.

Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.

Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

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Answer: 6/23  mph

Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.

Based on the fact that the identical darts were thrown at four identical dartboards and Ben took a list, the number of different lists possible is 5 lists.

If all the darts hit on dartboard then the list would be:

= 0004

If one dart hit a dartboard and three hit one dartboard the list would be:

= 0031

If two darts hit two boards:

= 0022

If two darts hit one board, 1 dart two others:
= 0211

If all darts hit separate boards;

= 1111

This means that 5 lists are possible to Ben.

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Answer:

y = 56/3

Step-by-step explanation:

We need to write equations to solve

Let the two numbers be x and y

The sum is 56

x+y = 56

The first number is 2 times greater than the second number.

x = 2*y

Substitute this into the first equation

x+y = 56

2y+y=56

3y = 56

y = 56/3

Step-by-step explanation:

Let the numbers be x and y

The sum of the two numbers is 56 :

Step 1:

X + Y = 56.......... (1)

Also, the first number is 2 times greater than the second number:

Step 2:

2X + Y = 0........... (2)

By substitution method, make Y the subject from (2)

Step 3:

Y = -2X .......... (3)

Put (3) into (1)

Step 4

X - 2X = 56

-X = 56

[tex] \frac{ - x}{ - 1} = \frac{56}{ - 1} [/tex]

X = -56

Put X=56 into (3)

Step 5

[tex]y = - 2( - 56)[/tex]

[tex]y = 112[/tex]

The second number is now 112.

Given :-

Solution :-

>> 2x + 5 < x + 1 / 4

>> 4 (2x + 5) < x + 1

>> 4 × (2x + 5) < x + 1

>> 8x + 20 < x + 1

>> 8x - x < 1 - 20

>> 7x < 1 - 20

>> 7x < -19

>> x = -19 / 7

[tex]\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}[/tex]

Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.

          [tex]\boldsymbol{\sf{8x+20 < x+1 }}[/tex]

Resta x en los dos lados.

              [tex]\boldsymbol{\sf{8x+20-x < 1 }}[/tex]

Combine 8x and −x to get 7x.

                [tex]\boldsymbol{\sf{7x+20 < 1 }}[/tex]

Subtract 20 on both sides.

                 [tex]\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}[/tex]

                  [tex]\boldsymbol{\sf{7x < -19 }}[/tex]

Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.

                     [tex]\boldsymbol{\sf{x < -\dfrac{19}{7} } }[/tex]

As the end result, it is not simplified or divided, then

                               [tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}[/tex]

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k  is this series written in sigma notation.

What is the series written in sigma notation?

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k

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Answer:

27/31

Step-by-step explanation:

FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31

Answer:

16

Step-by-step explanation:

6/3 = 2 postcards per day

2x8 = 16 postcards

Answer: try 35

Step-by-step explanation:

Answer:

  d.  x = 5

Step-by-step explanation:

Chords that subtend congruent arcs are congruent.

Chord lengths are the same:

  AB = CD

  16x -2 = 14x +8

  2x = 10 . . . . . . add 2-14x

  x = 5 . . . . . . . . divide by 2

Statements that describe the given function are:

To find the statements that describe the given function:

Lastly, the correct answers are:

Therefore, statements that describe the given function are:

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The complete question is given below:

Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.

(A) f(x) has one real zero because it crosses the x-axis once.

(B) f(x) has two real zeros because it crosses the x-axis twice.

(C) f(x) has real zeros at 1 and –1.

(D) f(x) has a real zero at 2.5.

(E) f(x) has x-intercepts at (1, 0) and (–1, 0).

(F) f(x) crosses the x-axis when x = 1 and x = –1.

(G) f(x) has an x-intercept at (2.5, 0).