The blue dot is at what value on the number line?
-10
-6

An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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0.92

Step-by-step explanation:

There are 4 cards in a deck of 52 cards that has a face value of 3. That means that the other 48 cards don't have a face value of 3. Therefore, the probability of picking a card of this deck that doesn't have a face value of 3 is

\(P =\dfrac{48}{52} = 0.92\)

The probability that the card does not have a face value of 3 is 0.92.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the card does not have a face value of 3 - (total cards in a deck of cards - number of cards with a face value of 3) / total cards in a deck of cards

(52 - 4) / 52

= 48 / 52 = 0.92

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he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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The width of the rectangle whose perimeter is 37 cm is 6.25 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The length of a rectangle is 6 cm more than its width, w cm.

So, the length = w + 6

The perimeter of the rectangle is 37 cm.

Then, Perimeter of the rectangle = 37

2(l+ w) = 37

2( w+ 6 +w )= 37

2(2w + 6)= 37

4w + 12 = 37

4w = 25

w = 6.25 cm

and, length = w+ 6 = 6 + 6.25 = 12.25 cm

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Answer:

The c will equal 2.56

Step-by-step explanation:

The A will equal 42.48 degrees

The B will equal 96.92 degrees

The combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

To calculate the combined balance of both bank accounts after 3 years, we'll calculate the balance for each account separately and then add them together.

For Bank A, we can use the compound interest formula:

A =\(P(1 + r/n)^(nt)\)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

n = number of times that interest is compounded per year

t = number of years

In this case, Wanda deposited $370 at a 2.25% interest rate compounded annually, so we have:

P = $370

r = 2.25% = 0.0225 (as a decimal)

n = 1 (compounded annually)

t = 3 years

Using the formula, we can calculate the balance for Bank A:

A_A = \(370(1 + 0.0225/1)^(1*3)\)

=\(370(1.0225)^3\)

= 370(1.0678450625)

= $394.76

For Bank B, we can use the simple interest formula:

A = P(1 + rt)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

t = number of years

In this case, Wanda deposited $600 at a 2.5% simple interest rate, so we have:

P = $600

r = 2.5% = 0.025 (as a decimal)

t = 3 years

Using the formula, we can calculate the balance for Bank B:

A_B = 600(1 + 0.025*3)

= 600(1.075)

= $645

Finally, we can calculate the combined balance of both bank accounts:

Combined Balance = A_A + A_B

= $394.76 + $645

= $1039.76

Therefore, the combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

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Answer:

2.5 us dollars

Step-by-step explanation:

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

The correct answer is:

Option H: 7(x − 3) and 7x − 7 • 3

Step-by-step explanation:

Equivalent expressions are those expressions that simplify to the same expression i.e. the result of both expressions is the same. There is no change of sign or variable or any quantity.

Option H:

The two expressions are:

7(x − 3) and 7x − 7 • 3

\(7(x-3) = 7x - 21\\7x - 7.3 = 7x-21\)

It can clearly be seen that both the expressions result in same expression

Hence,

The correct answer is:

Option H: 7(x − 3) and 7x − 7 • 3

Simple Interest formula:

Where

i is the interest earned

P is the initial amount

r is the rate of interest per year, in decimal

t is the time in years

Given, in the problem,

P = 75,266

r = 14% = 0.14

t = 4 yrs

We find the interest amount earned in 4 years to be:

So, total amount of money in the account at the end of 4 years is initial PLUS the interest earned.

75266 + 42148.96 = $117414.96

(i) 47 * 1 = 47

Why? This is because the Multiplication Identity Property states that any number w multiplied by 1 is equal to w

(ii) 135 * 0 = 0

Why? The Zero Property of Multiplication states that 0 multiplied by any number is 0.

(iii) 3 * 5 = 5 * 3

Why? The order numbers are multiplied in does not impact the answer's value according to the Commutative Property of Multiplication

(iv) 7 + 0 = 7

Why? The Zero Property of Addition states that 0 added to any number x is equal to x

(v) 125 * 315 - 125 * 215 = 125 * (315 - 215) = 12500

Why? The Distributive Property states that a * c - a * b = a * (c - b).

Answer:

m = - 5

Step-by-step Explanation:

\(-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}\)

Answer:

-5

Step-by-step explanation:

sec(theta) = 1/cos(theta)

I believe that is your option D

Answer:

increase = New number - original number

inc % = (increase ÷ original number) *100%

Step-by-step explanation:

133 - 76 = 56

inc % = 57 ÷ 76 = 0.75

0.75*100% = 75%

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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Answer:

Kendall

Step-by-step explanation:

Cmxmx

Answer:

B

Step-by-step explanation:

I made a 100

Answer:

Step-by-step explanation:

a)  27 = 3 × 3 × 3 = 3³    Answer: 3

b)  32 = 2 × 2 × 2 × 2 × 2 = \(2^5\)     Answer: 5

c) 625 = 5 × 5 × 5 × 5 = \(5^4\)     Answer: 4

d) \(\sqrt{64} = 8 \)  ⇒  \(64^{\frac{1}{2}} \)    Answer: 1/2

e) \(\sqrt[4]{81}=3 \)  ⇒  \(81^{\frac{1}{4}} \)   Answer: 1/4

f) \(\sqrt[6]{64} =2\)  ⇒  \(64^{\frac{1}{6} }\)    Answer: 1/6

g) \((x^2)^{\frac{1}{2}}=x^1=x \)     Answer: 1/2

h)  \((x^3)^{4}=x^{12}\)    Answer: 4

i)  \((x)^8=x^8\)   Answer: 8

Answer:

Step-by-step explanation:

Prime factorize 27,32,625,

a) 27 = 3 * 3 * 3 = 3³

b) 32 = 2 * 2 * 2 * 2 *2 = 2⁵

c) 625 = 5*5*5*5 = 5⁴

\(d) \sqrt{64}= (8^{2})^{\frac{1}{2}} = 8\\\\ e) \sqrt[4]{81}=\sqrt[4]{3*3*3*3}=(3^{4})^{\frac{1}{4}} = 3\\\\ f) \sqrt[6]{64}=\sqrt[6]{2*2*2*2*2*2}=(2^{6})^{\frac{1}{6}}=2\\\\ g)\sqrt{x^{2}}=(x^{2})^{\frac{1}{2}}=x\\\\ \)

\(h) x^{12} = x^{3*4}= (x^{3})^{4}\\\\ i)x^{8}=x^{1*8}=(x^{1})^{8}\)

Answer:

1/5

Step-by-step explanation:

total CDs = 6 + 10 + 4 + 8 + 12 = 20 + 20 = 40

hip hop = 8

8/40

(8:8)/(40:8)

1/5

Answer:

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\) in the factored form will be:

Step-by-step explanation:

Given the function

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\)

Use the rational root theorem.

\(a_0=22,\:\quad a_n=1\)

\(\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:11,\:22,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1\)

\(\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:11,\:22}{1}\)

\(-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\)

\(=\left(x+2\right)\frac{x^3-4x^2-x+22}{x+2}\)

as

\(\frac{x^3-4x^2-x+22}{x+2}=x^2-6x+11\)        ∵ \(x^3-4x^2-x+22=\left(x+2\right)\left(x^2-6x+11\right)\)

so the expression becomes

\(x^3\:-\:4x^2\:-\:x\:+\:22=\left(x+2\right)\left(x^2-6x+11\right)\)

Therefore,

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\) in the factored form will be:

Answer:

12

Step-by-step explanation:

Answer:

Your answer is:

1) 0.75  *  2

2) 0.3  *  5

Step-by-step explanation:

Hope any of these helped you : )

Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.

What is deviation ?

Deviation refers to how far a value or set of values is from the mean or average. In statistics, the standard deviation is a measure of the spread of a dataset, calculated as the square root of the variance. It represents the average distance of each data point from the mean. A low standard deviation indicates that the data points tend to be close to the mean.

To compute the probabilities for a standard normal random variable, we can use a standard normal table or a calculator with standard normal distribution functions.

P(z ? -1.0) = P(z < -1.0) = 0.1587

P(z ? -1.0) = P(z > -1.0) = 1 - 0.1587 = 0.8413

P(z ? -1.5) = P(z < -1.5) = 0.0668

P(z ? -2.5) = P(z < -2.5) = 0.0062

P(-3 < z ? 0) = P(-3 < z < 0) = P(z < 0) - P(z < -3) = 0.5 - 0.0013 = 0.4987,

Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The expression for the area enclosed between the two squares with respect to the rotation angle α is

(α/90)a².

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side²

We have,

Side of the square = a

Area of the square = a²

The full angle that can be rotated is 90°.

Now,

The area enclosed if the angle is 90°.

= a²

We can write as,

The area enclosed in terms of the angle.

= (angle rotated / 90) x side²

= (angle rotated / 90) x a²

Now,

The angle rotated is α.

The area enclosed is (α/90)a².

Thus,

The expression for the area enclosed between the two squares with respect to the rotation angle α is

(α/90)a².

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Answer:

I guess it's False...Hope it helps you.

Answer:

true

Step-by-step explanation:

Answer:

Wavelengths of all possible photons are;

λ1 = 9.492 × 10^(-8) m

λ2 = 1.28 × 10^(-6) m

λ3 = 1.28 × 10^(-6) m

λ4 = 4.04 × 10^(-6) m

Step-by-step explanation:

We can calculate the wavelength of all the possible photons emitted by the electron during this transition using Rydeberg's equation.

It's given by;

1/λ = R(1/(n_f)² - 1/(n_i)²)

Where;

λ is wavelength

R is Rydberg's constant = 1.0974 × 10^(7) /m

n_f is the final energy level = 1,2,3,4

n_i is the initial energy level = 5

At n_f = 1,.we have;

1/λ = (1.0974 × 10^(7))(1/(1)² - 1/(5)²)

1/λ = 10535040

λ = 1/10535040

λ = 9.492 × 10^(-8) m

At n_f = 2,.we have;

1/λ = (1.0974 × 10^(7))(1/(2)² - 1/(5)²)

1/λ = (1.0974 × 10^(7))(0.21)

1/λ = 2304540

λ = 1/2304540

λ = 4.34 × 10^(-7) m

At n_f = 3, we have;

1/λ = (1.0974 × 10^(7))(1/(3)² - 1/(5)²)

1/λ = (1.0974 × 10^(7))(0.07111)

1/λ = 780373.3333333334

λ = 1/780373.3333333334

λ = 1.28 × 10^(-6) m

At n_f = 4, we have;

1/λ = (1.0974 × 10^(7))(1/(4)² - 1/(5)²)

1/λ = (1.0974 × 10^(7))(0.0225)

1/λ = 246915

λ = 1/246915

λ = 4.04 × 10^(-6) m

Answer:

Step-by-step explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

  The range is {y l y ≤ 6}.

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

  The function is increasing over the interval (-∞, -2).

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

  The function has a positive y-intercept.

The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

Given that,

The following information was discovered after applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

y=12+1.8x

n=17

SSR=225

SSE=75

S₀₁=0.2683

We have to find what is the t statistic used to determine whether the slope is significant.

We know that,

Given by, the t test is used to determine whether the slope is significant.

t= b1/s.e

Where b1= slope of the given regression line

s.e= standard error of the line ( Sb1)= 0.2683

The regression line is given by

Y=12+1.8X

X is the independent variable here, and Y is the dependent variable.

Intercept = 12

Slope = 1.8

The t test is used to determine whether the slope is significant.

t= b1/s.e=1.8/0.2683= 6.7089=6.709

Therefore, The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

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Answer:

5*a+10*b=12,

a+b=1.5

Step-by-step explanation: