A mattress store is having a sale. All mattresses are 30% off. Nate wants to know the sale price of a mattress that is regularly $1,000.


How much is the discount? Enter the amount in the table.

The given expressions are the results of applying the function f to a value that is being multiplied by -3 or 3.

f(-3x) means that the function is applied to -3x, in this case the output is -3f(x)

f(3x) means that the function is applied to 3x, in this case the output is 3f(x)

It should be noted that the function f(x) could be any type of function and the output depends on the function's definition.

Answer: 3x^2

Step-by-step explanation:

e2023

The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

The annual percentage rate, or APR, is the interest rate that is charged on a loan balance that is still outstanding. The expected cost of the annual fees connected with a certain sort of borrowing is what the APR conceptually reflects.

APR is a commonly used formula by lenders that enables borrowers to compare various loan choices. The stated interest rate on a loan is typically insufficient on its own to help borrowers choose the best loan option.

A loan with a low stated interest rate could also have significant costs attached that should not be disregarded. The best alternative might be a loan with a smaller fee structure and a higher advertised interest rate. APR is calculated as (Periodic Interest Rate x 365 Days) x 100 i.e.

[tex]$\mathrm{APR=\left(\left(\frac{\frac{Fees+Interest}{Principal}}{n} \right) \times 365 \right) \times 100}[/tex]

​where:

Interest = Total interest paid over life of the loan

Principal = Loan amount

n = Number of days in loan term

Fees = 0

​Interest = 2​Interest = $519.48

Principal = $624.00

n = 52 × 7 = 364 days

Plug the data in the formula:-

[tex]$\mathrm{APR=\left(\left(\frac{\frac{0+519.48}{624}}{364} \right) \times 365 \right) \times 100}[/tex]

APR = 83.48%

Thus, The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

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If a = the measure of the smaller angle, we have:

[tex]\it a+2a+9^o=180^o\bigg|_{-9^o} \Rightarrow 3a=171^o\bigg|_{:3} \Rightarrow a=57^o[/tex]

To graph a linear inequality in slope intercept form:

The solutions that make both inequalities true are all shown on the graph of an inequality system. When you are graphing inequalities, keep the following in mind: Form your inequality as y=mx+b, the slope intercept. Either the equal sign or the provided inequality symbol may be used.

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Answer:

x > -1

10 ≤ d

k ≤ -24

Step-by-step explanation:

a)

13 + 4x > 9

4x > -4

x > -1

b)

99 - 5d ≤ 4d

99 ≤ 9d

10 ≤ d

c)

3k - 9 ≤ -6k - 225

3k + 6k ≤ 9 - 225

9k ≤ -216

k ≤ -24

Answer:

Nabila has $25 dollars.

Hasan has $19 dollars.

Tarek has $50 dollars.

Step-by-step explanation:

Let's say Hasan has "x" dollars at first. The question tells us that Nabila has six more dollars than Hasan has. This means that Nabila has "x + 6" dollars. The last given information is that Tarek has two times what Nabila has. So, Tarek has "2x + 12" dollars, basically.

Then, we can add up all these amounts to find out the result for each person.

We found what is "x". This means that we actually found the answer.

Hasan had "x" dollars so he has $19 dollars.

Nabila had "x + 6" dollars so she has $25 dollars.

Finally, Tarek had "2x + 12" dollars or two times of what Nabila has so he has $50 dollars.

The slope intercept form of the equation of the line graphed on the coordinate plane below will be y=-3x -1.

As we know, The slope intercept form of a straight line is y=mx + c, where m is the gradient which is the Tanθ where θ is the angle between the line and the x-axis. And C is the interception point on the y-axis.

To find the gradient, we can calculate Δy/Δx. From the graph given we can take two points on the line with the coordinates (1,-4) and (0,-1). From this, we can calculate the gradient :

⇒[tex]\frac{(y2-y1)}{(x2-x1)}[/tex]

⇒[tex]\frac{(-1)-(-4)}{0-(1)}[/tex]

⇒-3

And , from the figure we can see the line is intersecting the y-axis -at -1.

So, putting the values in y=mx+c will give us y=-3x -1

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Let u and v be a vectors. Then u can be broken up into two components, r and s such that r is parallel to v and s is perpendicular to v.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

In particular, u (v w) makes no sense if u, v, and w are vectors because v w is a scalar. Before confirming that the dot product has the desired geometric characteristics, we'll mention.

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When given vector u = (1, 2) and v = (1, -4), Then the value of 4u + 3v = ⟨7, -4⟩, graph in attachment.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

Given u = (1, 2) and v = (1, -4),

4u + 3v = 4(1, 2) + 3(1, -4)

= (4, 8) + (3, -12)

= ⟨4 + 3, 8 + (-12)⟩

= ⟨7, -4⟩

Thus, 4u + 3v = ⟨7, -4⟩

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A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.

Mathematically, the point-slope form of any straight line can be calculated by using this expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on this line:

At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(2 - 0)(x - 0)

y - 3 = -3/2(x)

y = -3x/2 + 3

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Answer:

Step-by-step explanation:

A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.

What is the point-slope form?

Mathematically, the point-slope form of any straight line can be calculated by using this expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.

x and y represents the data points.

From the information provided above, we have the following slope and data points on this line:

Points on x-axis = (0, 2).

Points on y-axis = (3, 0).

At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(2 - 0)(x - 0)

y - 3 = -3/2(x)

y = -3x/2 + 3

Expanding, which entails multiplying out the factors, allows an equation in factored form to be rewritten in standard quadratic form.

The steps we employ in doing so are as follows:

Opposite of expanding is factoring an expression. Parenthesis or grouping symbols are removed from an expression when it is expanded. The Greatest Common Factor (GCF) from each phrase allows each extended statement to be factored.

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Answer:Answers below

Step-by-step explanation:

The average age of the zebras at the zoo can be found by adding up all of the ages and dividing by the number of zebras.

In this case, the ages of the zebras are 8, 11, 17, 7, 19.

To find the average age, we add up all of the ages: 8 + 11 + 17 + 7 + 19 = 62

Then we divide by the number of zebras (5): 62/5 = 12.4

So, the average age of the zebras at the zoo is 12.4 years old.

To find the standard deviation, we first need to find the variance.

The variance is the average of the squared differences from the mean.

We can find the variance by taking each value, subtracting the mean, squaring the result, and dividing by the number of zebras.

The standard deviation is the square root of the variance

So, the standard deviation of the zebras age is difficult to calculate by hand, but we can use a calculator to find the standard deviation, which is approximately 4.345 years.

Rounding to the nearest tenth:

The average age is 12.4 years old

The standard deviation is 4.3 years

Answer: (9.5, 24)

Step-by-step explanation:

10x + 7y = 263           (1)

4x + 8y = 230              (2)

Multiply (1) by 4 and (2) by 10:

40x + 28y = 1052             (3)

40x + 80y = 2300              (4)

Do (4) - (3):

52y = 1248

y = 24

x = 9.5

(x, y) = (9.5, 24) :>

For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is, 18/60.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Total number of tossing a number cube = 60

Here, Number of times greater than 4 comes up = 10 + 8 (frequency of is 10 and frequency of 6 is 8)

Hence, Number of times greater than 4 comes up = 18

Thus, Probability of getting number greater than 4

=  (frequency of getting 5 and 6) / (total number of trials)

Hence, Probability of getting number greater than 4  = 18 / 60                                                                      

Therefore, For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

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Answer:

.125%

Step-by-step explanation:

Answer:

To find the percent of tourists buried up to their neck in sand, you can divide the number of buried tourists by the total number of tourists and multiply by 100.

12 buried tourists / 9,600 total tourists = 0.00125

0.00125 x 100 = 0.125 or 12.5%

So, 12.5% of the tourists were buried up to their neck in sand.

Answer:

when x = 12, a = 360 and b = 16.8.

Step-by-step explanation:

Answer:

15.87% (2 d.p.)

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of adult male rhesus monkeys are normally distributed:

[tex]\boxed{X \sim\text{N}(17, 3^2)}[/tex]

where X is the weight of an adult male rhesus monkey.

To calculate the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds, we need to find P(X < 14).

Calculator input for "normal cumulative distribution function (cdf)":

⇒ P (X < 14) = 0.158655253...

⇒ P (X < 14) = 15.8655253...%

⇒ P (X < 14) = 15.87%

Therefore, the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds is approximately 15.87% (2 d.p.).

Answer:

f = 53.13 degrees

Step-by-step explanation:

An isosceles triangle has two equal sides, so in this case the sides of length 60cm are equal. The base angle (f) is opposite the base of the triangle, which is the side of length 100cm.

To find the base angle, we can use the law of cosines.

c^2 = a^2 + b^2 - 2ab*cos(f)

where c is the hypotenuse (the side of length 100cm), a and b are the legs (the sides of length 60cm), and f is the base angle we are trying to find.

Substituting in the given values, we get:

100^2 = 60^2 + 60^2 - 2(60)(60)cos(f)

Simplifying this equation, we get:

10000 = 3600 - 3600cos(f)

so

cos(f) = (10000-3600)/3600 = 6400/3600 = (8/3)^2

then

f = cos^-1((8/3)^2)

Therefore, f = 53.13 degrees

Answer:

Quadrilateral

Step-by-step explanation:

I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.

The leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

What is function ?

function can be defined in such a way that it relates an input to the output.

Given function y = x-3

The degree of the function means the highest power of the variable

Here, the degree is 1, it is odd.

The leading coefficient is 1, which is positive.

By taking sample values of x, we get values of y with the graph as shown

From the graph, we can say that the degree of the function is odd, so the ends of the graph continue in opposite directions

Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

The following describes the function x-3  that the degree of the function is odd, so the ends of the graph continue in opposite directions.

Hence,  the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

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Answer:

$77.5

Step-by-step explanation:

Has risen in price BY 310% To mean its price has added 310% from the old price:

Price new = Price old + (Price old × 310%).

To calculate the difference, we just need to calculate 310% of the old price (a percentage is a hundredth):

$25 × 310% = $25 × 3.1 = $77.5

For the roots to be real and equal, the value of k should be 9, -9.

The complete question is:

For what values of k are the roots of the quadratic equation 3x2 + 2kx + 27 = 0 real and equal?      

For the roots of the equation to be real and equal, we first compare the given quadratic equation with standard form of quadratic equations, which is: [tex]ax^2+ bx+ c=0[/tex]

Thus, a = 3; b= 2k and c = 27

We know, for real and equal roots, Discriminant (D) = [tex]b^2 - 4ac[/tex] = 0

Therefore, we now substitute the values of a, b, and c in the above formula, we get

(2k)^2 - 4(3)(27) = 0

4k^2 - 324 = 0

4k^2 = 324

k^2 = 81

k= 9 or -9

Thus, the value of k is 9 or -9.

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By applying the division formula, the number of times the ferry crossed the river would be 6 times.

To divide something means to split it into two or more equal pieces, areas, classes, categories, groups, or divisions. Dividing something means to give each component to a separate group, or to create equal parts from the whole. When doing division, the resulting value may or may not be an integer. The final result may occasionally be expressed as a decimal.

To calculate the division, we can use this following formula:

Dividend ÷ Divisor = Quotient + Remainder.

Where:

Dividend = the number, which is being divided

Divisor = the number, which divides the number (dividend) into equal parts

Quotient = the result of the division operation

Remainder = the leftover number in the division operation.

In this case, we are given that:

Dividend = 150

Divisor = 25

Thus, the number times the ferry crossed the river would be:

= 150 ÷ 25

= 6

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The domain is the set of all x-values (or inputs) used by the function.  In a graph like this, you want to see how the graph lines up with the x-axis.  

As an interval, the domain is [-4,-1], as shown on the domain graph.
(Remember to write intervals from lesser-to-greater.)

The range is the set of all y-values (or outputs) used by the function.  In a graph like this, you want to see how the graph lines up with the y-axis.  

As an interval, the range is [-4,-2].  
(Again, remember to write intervals from lesser-to-greater.)

Answer:

£1885.71

Step-by-step explanation:

Reducing by 30% is doing this: 100% - 30% = 70% = 0.7

Reducing a price by 30% is the same as multiplying the price by 0.7

Adding 17.5% is doing this: 100% + 17.5% = 117.5% = 1.175

Adding 17.5% to a price is the same as multiplying the price by 1.175

Let the original price be x.

1.175 × 0.7 × x = £1551

x = £1551/(1.175 × 0.7)

x = 1885.71

Answer: £1885.71

Answer:

14.0cm

Step-by-step explanation:

if 13.8 = 12.0

then 16.1 = ?

[tex] \frac{16.1}{13.8} \times 12.0cm = 14.0cm [/tex]

Answer:

14 cm

Step-by-step explanation:

1st plant:

13.8 - 12.0 = 1.8

1.8/12 = .15

.15 x 100 = 15% growth

2nd plant:

let x =  original height

x + x(.15) = 16.1

1.15x = 16.1

x = 16.1 / 1.15 = 14.0 cm

Ratio of sine of angle of incidence to the sine of angle of refraction is constant by Snell’s law.

According to Snell's Law, the refractive index, or n, is a constant that represents the ratio of a wave's angle of incidence to angle of refraction as it passes through a boundary between two mediums.

₁n₂=n₂/n₁=sin θ₁/sin θ₂= v₁/v₂,

where n is the refractive index,

v is the speed in different medium and θ is the angle between the normal and the ray at the surface of boundary.

If we do an experiment and measure the angles of incidence and refraction, we will discover that a straight line passing through the origin results from plotting the sine of the angles of incidence and refraction.

This shows that the sine of the angle of incidence and the sine of the angle of refraction are directly related, and that the ratio of the two will result in a constant value that we refer to as the refractive index. The ratio of the sines of the angles corresponds to the proportion of the wave speeds through the medium.

Thus, we can say that refractive index is constant for a given pair of media.

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The translation and rotation of 180° about the origin. Then the correct option is A.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

From the graph, the trapezoid W'X'Y'Z' is derived by the translation and rotation of 180° about the origin. Then the correct option is A.

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Answer:

of course it would be 45

Step-by-step explanation:

it right trusss