A television has a normal price of £670. In a sale the price is reduced by 30%. Work out the price of the television in the sale.

a) The least squares estimate of the slope (b₁) can be calculated using the formula:

b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)

Where n is the number of observations, x and y are the explanatory and response variables, respectively.

b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8

b) The least squares estimate of the intercept (b₀) can be calculated using the formula:

b₀ = (∑y - b₁*(∑x))/n

b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4

c) The point estimate of y when x=2 can be calculated using the equation of the line:

y = b₀ + b₁x

y = 3.4 + 0.82 = 4.8

So the point estimate of y when x=2 is 4.8

In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.

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Answer:

2

Step-by-step explanation:

- 4m + 5 = 3m - 9

3m - 9 = 5 - 4m

3m + 4m = 5 + 9

7m = 14

m = 14 / 7

m = 2

Answer:

theres an black screen

Step-by-step explanation:

mark as brainliest!!

Answer:

Cant see the image

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

Prime Factors of 545 are 5, 109, and usually expressed as 5 x 109. 4.

hope this is right! :) -liaa

Answer:

Read below.

Step-by-step explanation:

4000÷5=800

If it costs APPLE $4000 for those 10 iPads, then it will cost the consumers:

800+225=$1025

If it costs the CONSUMERS $4000 for the 10 iPads, then it costs Apple:

800-225=$575 for each iPad

We can conclude that both plans, A, and B last for 45 minutes.

So, according to the information, we will form the two equations:

To solve this system of equations, multiply both sides of one equation so that there is only one variable present when the equations are added or subtracted.

We will multiply -3 by both sides of the 2ndequation.

Now, by adding the two equations, we will eliminate the variable b.

Now, substitute 3/4 as an into one of the initial equations to find b.

The second original equation will be applied.

The duration of both exercise programs is the same.

Therefore, Plan A and Plan B both last for 45 minutes.

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Answer:

below

Step-by-step explanation:

2x-y =14

-3x+y = -6     add these two equations together....this will 'eliminate' y

-x = 8

x = -8    use this value of x in one of the equations to find y = -30

The z-score for this amount of advertising time is z = -4.17 so option B is correct.

Given:

Average = 13 minutes

Standard deviation = 1.2 minutes.

Advertising time x = 8 minutes.

z = x - mean / standard deviation.

= 8 - 13/1.2

= -5/1.2

= -5/12/10

= -50/12

= -4.17.

Therefore the z-score for this amount of advertising time is z = -4.17 so option B is correct.

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Answer:

1389

Step-by-step explanation:

hope this helps?

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

f(9) = 189

Step-by-step explanation:

Plug 9 into x

f(9) = 2(9)^2 + 3(9)

f(9) = 2(81) + 27

f(9) = 162 + 27

Thus, f(9) = 189

Answer:

189

Step-by-step explanation:

f(x) = 2x^2 + 3x , f(9)

f(9) = 2(9)^2 + 3(9)

= 2(81) + 27

= 162 + 27

= 189

Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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Answer:

c. 84 ft²

Step-by-step explanation:

lateral area = 1/2 * base perimeter * height

where

base sides = 6 ft.

height (L) = 7

lateral area = 1/2 x (4*6) * 7

lateral area = 84 ft²

LA = 1/2pl

p = base perimeter

l = length

p = (6 * 4)

p = 24

l = 7

Use the formula and solve.

LA = 1/2(24)(7)

LA = 1/2(168)

LA = 84

Therefore, the answer is C

Best of Luck!

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

Answer:

6

Step-by-step explanation:

Add all the numbers together and divide by the amount of numbers

6+9+3+8+9+3+4= 42

42/7 = 6

Answer:

6

Step-by-step explanation:

To find the mean or the average of the data set, you add all the numbers together and then divide the sum by the number of numbers in the data set.

6+9+3+8+9+3+4 =42

Then divided by the # of terms.

42/7= 6

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

 =  − 1

Step-by-step explanation:

Answer:

If we're taking in terms of square roots (that are in the equation I'm working with), then your answer would be:

x = -12

Answer:

64°

Step-by-step explanation:

If two angles add up to give 90°, that are said to be complementary. One is a complement of the other.

Therefore, given that the measure of an angle, angle A = 26°, the measure of the complement of angle A = 90 - 26 = 64°.

The measure of the complement of angle A, is 64°.

Answer:

\(P(x\geq 3)=0.3233\)

Step-by-step explanation:

If the number of defects in poured metal follows a Poisson distribution, the probability that x defects occurs is:

\(P(x)=\frac{e^{-m}*(m)^{x}}{x!}\)

Where x is bigger or equal to zero and m is the average. So replacing m by 2, we get that the probability is equal to:

\(P(x)=\frac{e^{-2}*(2)^{x}}{x!}\)

Finally, the probability that there will be at least three defects in a randomly selected cubic millimeter of this metal is equal to:

\(P(x\geq 3)=1-p(x\leq 2)\\\)

Where \(P(x\leq 2)=P(0)+P(1)+P(2)\)

So, P(0), P(1) and P(2) are equal to:

\(P(0)=\frac{e^{-2}*(2)^{0}}{0!}=0.1353\\P(1)=\frac{e^{-2}*(2)^{1}}{1!}=0.2707\\P(2)=\frac{e^{-2}*(2)^{2}}{2!}=0.2707\)

Finally, \(P(x\leq2)\) and \(P(x\geq3)\) are equal to:

\(P(x\leq 2)=0.1353+0.2707+0.2707=0.6767\\P(x\geq 3)=1-0.6767=0.3233\)

Answer:

i did'nt understand the question

Step-by-step explanation:

sorry

Answer:

The negation is the OPPOSITE of whatever is said, so in this case, the opposite of "Not all rooms at the hotel have a bed." would be D "All rooms at the hotel have a bed" and A "No room at the hotel has a bed"

The correct answers are A and D

Let me know if this helps!

Answer:

a. no because it states that no rooms have a bed when it states not all rooms at the hotel have a bed

b. yes because while its true some rooms dont have a bed other rooms will

c. yes again some rooms do have a bed and some dont

d. no because we have already established that only some rooms have beds not all

hope this helps

Step-by-step explanation:

The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.

Let A denote the event that a student does not have a sibling.

Let B denote the event that a student has a pet.

Then A∩B will denote the event that the student does not have a sibling but he has a pet.

Let P denote the probability of an event in this question.

Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.

P(B|A)

We know that:

\(P(B|A) = \frac{P(A\cap B)}{P(A)}\)

Also from the table, we have:

P(A)=0.25

and P(A∩B)=0.15

Hence,

\(P(B|A) = \frac{0.15}{0.25}\)

\(P(B|A) = \frac{3}{5}\)

\(P(B|A) = 0.6\)

which in percentage is:

0.6 * 100 = 60 %

Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.

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\((\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{4}}}\implies \cfrac{4+2}{-6}\implies \cfrac{6}{-6}\implies -1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4}) \\\\\\ y+2=-x+4\implies y=-x+2\)

Cost of 14 songs = $9.38

So, cost of 1 song

= $9.38/14

= $0.67

So, each sing costs $0.67.