A 9-inch candle burns down in 6 hours. How far has it burned after 5 1/2​ hours? Use the dropdown menu to state your answer as a decimal, mixed number, or improper fraction.

The statement that correctly compares the function of the given graph with the function y = 2x - 5 is; Option C: The function shown on the graph has a greater rate of change and a higher starting point.

The rate of change of function is defined as the change in the value of the function with respect to x value.

Rate of change of function f(x) is;

f'(x) = df(x)/dx

The given function is;  y = 2x - 5

Thus;

Rate of change of function = f'(x) = df(x)/dx = dy/dx = d(2x - 5)/dx = 2

The starting point of the function f is the y-intercept of the function.

The y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.

Thus; y = 2*0 - 5

y= -5

The starting point of function is -5.

Slope = (y intercept)/(x - intercept)

Slope = 4/1 =4

Thus, the rate of change of the graph = slope of the graph= 4

The y-intercept of the graph is equal to the starting point of the graph which is -5

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Answer:

true false false true true

Look to the photo and you will find the answers there ✔️

start from left to right

Answer:

It's the digit 3.

Step-by-step explanation:

Since all digits from 33 to 38 are digits not less than 3, it follows that in the result there will be at least one digit bigger than 3. Since 33 to 38 represent a set with six numbers, we can conclude that the product of those numbers must have at least six digits to the left of the decimal, which is the ones place. Therefore, the digital 3 gets into the ones place.

If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.

In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.

Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).

This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).

From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:

Area to the left of z-score (z₁ = 1.13) = 0.8708.

Probability, P(z ≤ 1.13) = 0.8708.

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The value of Priya's investment at end of the year is Rs. 24300.

The formula for simple interest is given by

Where, P = Principal amount, T = Time period, and R = Rate of interest  

And the formula for the Amount at end of the time period is given by

Here we have

Priya invests a sum of money at an interest rate of 8% per annum

The interest that she gained after 1 year = 1800 Rs.

Let P be the principal amount i.e Priya's investment

Then calculate Simple interest on P at 8% for 1 year

As we know Simple interest = PTR/100    

Interest on P = P(1)(8)/100 = 0.08P

From the given data, interest at end of the year = Rs. 1800

=> 0.08P = 1800

=> P = 1800/0.08

=> P =  22500  

The amount that Priya invested = Rs. 22500

As we know Amount = Principal amount + interest

= Rs. 22500 + Rs. 1800

= Rs. 24300  

Therefore,

The value of Priya's investment at end of the year is Rs. 24300.    

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Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08

The linear equation to model the scenario -

For the stated question;

Let the side of the equilateral triangle be 'x'.

Then,

Perimeter of the equilateral triangle = x + x + x

Perimeter of the equilateral triangle P = 3x

Now,

One side of rectangle = side of equilateral triangle = x.

Second side of rectangle = 6 + side of equilateral triangle = 6 + x.

Perimeter of the rectangle P = x + x + 6 + x + 6 + x

Perimeter of the rectangle P = 4x + 12

Thus, linear equation to model the scenario -

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 - x =< y is the expression and acceptable syntax.

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.

A term may be a number, a variable, a product of two or more variables, or a combination of both. A single phrase or a set of terms can make up an algebraic expression. The two terms in the formula 4x + y, for instance, are 4x and y.

Algebra's associative, commutative, and distributive characteristics are the ones that are most frequently utilized to make algebraic expressions simpler.

The converse of the expression and having proper syntax is

   = x >= y.

   = -x <= y

    =- x =< y

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Answer: Rs 60500

Step-by-step explanation:

Principal = Rs 50000 = p

Time = 7 years = t

Simple interest rate = 3% = r

Interest = p*t*r/100

using above formula,

50000*7*3/100=10500

So, final amount = principal + interest = 50000+10500 = Rs 60500

The mean yield for the three temperatures are equal.

Temperature is a unit used to express how hot or cold something is. It can be expressed using the Celsius or Fahrenheit scales, among others. Temperature shows which way heat energy will naturally flow, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given:

Number of groups [tex]k=3[/tex]

Number of observation in group 50°C, [tex]n_{1} =5[/tex]

Number of observation in group 60°C, [tex]n_{2} =5[/tex]

Number of observation in group 70°C, [tex]n_{3} =5[/tex]

Total number of observation [tex]N=15[/tex]

Null hypothesis [tex]H_{0}[/tex] :

The mean yield for the three temperatures are equal.

Alternative hypothesis [tex]H_{1}[/tex] : The mean yield for the three temperatures are not equal.

Now, Sum of the squares of between groups:

⇒∑  [tex]n_{i} (X_{i} -X)^{2}[/tex]

Here, [tex]X_{i}[/tex] is the mean of the jth group, [tex]X[/tex] is the overall mean and [tex]n_{1}[/tex] is the sample size of the jth group.

[tex]X=\frac{X_{1} +X_{2}+...+X_{i} }{i}[/tex]

[tex]X_{1} =34+24+36+39+32=165\\X_{2} =30=31+34+23+27=145\\X_{3} =23+28+28+30+31=140[/tex]

[tex]X_{i} =\frac{X_{i} }{n_{i} }[/tex]

⇒ [tex]X_{1} =\frac{165}{5} =33[/tex]

⇒ [tex]X_{2} =\frac{145}{5} =29[/tex]

⇒ [tex]X_{3} =\frac{140}{5} =30[/tex]

[tex]=n_{1} (X_{i} -X)^{2}+n_{2} (X_{2} -X)^{2}+n_{3} (X_{3} -X)^{2}[/tex]

SSB= 5 × [tex](33-30)^{2}[/tex]+ 5 × [tex](29-30)^{2}[/tex] + 5 × [tex](28-30)^{2}[/tex]

      = 5 × [tex]3^{2}[/tex] + 5 × [tex]1^{2}[/tex] + 5 × [tex]2^{2}[/tex]

      = 5 × 9 + 5 × 1 + 5 × 4

      = 45 + 5 + 20

      = 70

Now, Sum of difference between each element and grand mean squared (SST)

⇒ [tex](34-30)^{2} +(34-30)^{2}+(36-30)^{2} +...+(31-30)^{2}[/tex]

⇒ 306

Now, SSE = SST - SSB

= 306 - 70 = 236

Therefore,

Source of         Sum of                 Degrees of                   Mean

variation         squares             freedom                    square

Between      [tex]SSB=70[/tex]           [tex]df_{1} =k-1=2[/tex]            [tex]MSB=\frac{SSB}{df_{1} } =\frac{70}{2} =35[/tex]          

groups

Error    [tex]SSE=236[/tex]        [tex]df_{2} =N-k=12[/tex] [tex]MSE= \frac{SSE}{df_{2} } =\frac{236}{2} =19.67[/tex]                                          

Total                [tex]306[/tex]

Given .05 level of significance. i.e, [tex]F(0.05,2,12)=3.8853[/tex] tabulated value.

As [tex]1.7794 < 3.8853[/tex], tabulated value is higher than calculated value.

So, the null hypothesis is accepted.

Hence, the mean yield for the three temperatures is equal.

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The probability that a randomly selected american enjoys both activities is 23 % .

Given :

14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .

14 % = 0.14

48 % = 0.48

overlapping is 85 % = 0.85

P ( A ) = 0.14

P ( B ) = 0.48

P ( A and B ) = 0.85

we know that,

P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )

= 0.14 + 0.48 - 0.85

= 0.62 - 0.85

= -0.23

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The difference between the two confidence intervals is given as follows :

Width of confidence interval is directly proportional to confidence level.

This is because,  width is directly proportional to critical value (z or t), which is directly proportional to confidence level.

Now, width is inversely proportional to square root of sample size.

But if sample size is same for both levels of confidence. Then, sample size would have same effect.

Hence, the appropriate answer here is,

The 95 percent confidence interval will not be as wide as the 99 percent confidence interval.

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The Binomial expansion of given expression, (1+x)⁻¹ is 1 − x + x² - x³+ x⁴ + ...

Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y)ⁿ

Using the Binomial theorem we can expand the series of ( x + y )ⁿ as

( x + y)ⁿ = ∑ ⁿCₖ xⁿ⁻ᵏ yᵏ

k= 0 to n

= xⁿ + (n(n-1)/2!)x⁽ⁿ⁻¹⁾y + (n(n-1)(n-2)/3!)x⁽ⁿ⁻²⁾y² + .......

where n ≥ 0 and (ⁿCₖ ) is known as a binomial coefficient and they should be positive integers.

We have given that (1+x)⁻¹ comparing it with ( x + y )ⁿ we get, y = 1 ; n = -1

Binomial expansion for this is followed the same way as expanding larger power expansion,

So (1+x)⁻¹ = 1 + (-1)x + (-1)(-1–1)/2! x² + (-1)(-1–1)(-1–2)/3! x³+…….

= 1 -x + x²- x³ +….

but this will result in an infinite series and will converge for values belonging to

|x|<1. So, the required binomial series is

1 -x + x² - x³ +….

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Answer:  105 frames

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Given:  [tex]\textsf{25 frames per second, starts at 0 seconds already played 190 frames}[/tex]

Find: [tex]\textsf{Frame count already played when time = -3.4}[/tex]

Solution: In order to find the number of frames that have already played when the time was equal to -3.4 seconds, we must first figure out long the delay is.  We can do this by dividing 25 frames per second from 190 frames which gives us that 7.6 seconds passed before we started counting at 0.

Therefore, if we want to look at -3.4 seconds out of -7.6 seconds that means that 4.2 seconds passes after the initial playing to get to -3.4 seconds.  Now we can just multiply 4.2 seconds by 25 frames per second which gives us that about 105 frames have played when the time was equal to -3.4

The 2.5kg of potatoes cost £1.40 so the cost of 4.25 kg of potatoes is £2.38.

A cost is an outlay needed to create, market, or prepare an asset for regular use. In other words, it's the cost incurred to produce a good, buy inventory, sell goods, or prepare equipment for use in a business process.

Given,

2.5 kg of potatoes = £1.401 kg of potatoes

cost = 1.40/2.5

       = £0.56

To find the cost of 4.25 kg of potatoes is: Then,

1 kg = £0.564.25 kg

      = 0.56 x 4.25

      = £2.38

Thus from the above conclusion we can say that the cost is £2.38.

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The values for a and b in the expression for the area of the rhombus, a·√b, where the area of the regular hexagon that forms the rhombus that has an area of 24·√3, are; a = 8, b = 3

a + b = 8 + 3 = 11

A rhombus is a quadrilateral in which the length of the each of the four sides are the same.

Coprime integers integers are two integers that have 1 as their only common divisor

The area of the hexagons = 24·√3

The formula for the area of regular  hexagon, A = 3·√3×s²/2

Where;

s = The sider length of the regular hexagon

Therefore; 24·√3 = 3·√3×s²/2

The division property indicates that dividing booth sides of the above equation by √3, we get;

24 = 3×s²/2

2 × 24/3 = s²

16 = s²

s² = 16 (symmetric property)

s = ±√(16) = ±4

The possible value for the side length of the regular hexagon is +4

The formula for the area of a rhombus = s²·sin(θ)

Where;

θ = The interior angle of a regular hexagon = 120°

Therefore; A = 4² × sin(120°) = (16 × √3)/2 = 8·√3

Therefore; a·√b = 8·√3

a = 8, b = 3

a + b = 8 + 3 = 11

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Answer:

f(-1)= -1

Step-by-step explanation:

put -1 where x is

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

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

f(-1)= -3+2

f(-1)= -1

The rectangular prism has a capacity of 707.4 ft3  when it is fully filled with water.

Dimensions: 13.1 ft long, 7.5 ft wide, and 7.2 ft tall.

Thus:

Water volume equals 13.1 × 7.5 × 7.2

Water capacity is 707.4 feet3

Consequently, 707.4 ft3 of water will fit inside the rectangular prism when it is full.

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In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. Progressive Overload.

Progressive overload is the gradual increase of stress placed on the body during physical activity. By requiring the novice golfer to sink four consecutive putts before moving on to the next step, the study is increasing the difficulty of the task and placing additional stress on the body.

Progressive overload is an effective and essential technique for improving physical performance. It involves gradually increasing the intensity of the activity or exercise, which places additional stress on the body and forces it to adapt and become stronger. In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. This increased the difficulty of the task and allowed the golfer to gradually improve their performance. By gradually increasing the difficulty of the task, the study was able to effectively use progressive overload to improve the golfer's performance.

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The probability to win the game is 4/7.

Clearly, you can not win with zero dollars:

Pr(W|S0)=0

and you cannot lose with three dollars:

Pr(W|S3)=1

If you start with two dollars, then the probability of winning is:

Pr(W|S2)=Pr(S1|S2)Pr(W|S1)+Pr(S3|S2)Pr(W|S3)=1/3×Pr(W|S1)+2/3

If you start with one dollar, then the probability of winning is:

Pr(W|S1)=Pr(S2|S1)Pr(W|S2)+Pr(S0|S2)Pr(W|S0)=2/3×Pr(W|S2)

So, we have two equations in two unknowns:

Pr(W|S1)=2/3×Pr(W|S2)

Pr(W|S2)=1/3×Pr(W|S1)+2/3

Solving them we get:

Pr(W|S1)=4/7

Pr(W|S2)=6/7

So, your chance of winning when you start with one dollar is 4/7.

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The answer will be -6 when (16-24)-(57-77) divided by (-2).

What is division?

One of the basic mathematical operations is division, which splits a bigger number into smaller groups with the same number of components. For example, if 20 students need to be divided into groups of five for a sporting event, how many total groups will be created? Dealing with such challenges is made easier by the division operation. In this instance, divide 20 by 5. The result will be 20 x 5 = 4. There will be 4 groups total, each with 5 students. You can verify this number by multiplying 4 by 5 and getting the answer 20, which equals 20.

Here (16-24)-(57-77)/-2

= (-8)-(20)/-2

=12/-2

=-6

Hence the answer will be -6.

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The x-coordinate of the point K that divides AB in 3:1 will be -5.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The directions of the endpoints A and B are given. A (7,6) and B (- 9,- 6). Point K is situated on the Stomach muscle with the goal that AK: KB = 3/1.

Then the x-coordinate of the point K is given as,

x = (mx₂ + nx₁) / (m + n)

x = [3(-9) + 1(7)] / (3 + 1)

x = (- 27 + 7) / 4

x = - 20 / 4

x = - 5

The x-coordinate of the point K that divides AB in 3:1 will be -5.

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The quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.

ax2 + bx + c = 0 is a quadratic equation or a second-order polynomial equation with a single variable.

The algebraic's theorem guarantees that it is a second-order polynomial equation, hence it must have at least one solution.

The answer might be straightforward or challenging.

x2 - 5x - 3x + 15 = 0 are the roots of the quadratic equation x2 - 8x + 15 = 0.

x(x-5)-3(x-5)

(x-3)(x-5)=0

x = 3, 5

So, the correct answer is  x² - 8x + 15 = 0.

Therefore, the quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.

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Answer: 9:50 AM/PM

Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.

The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.

The rate will be:

= 1/4 ÷ 1/12

= 1/4 × 12

= 3

The correct option is C

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The probability that you land on 8 twice is 1/64

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We spin a spinner numbered 1-8 twice

The total sample space can be given by considering all the possible values

Hence the total number of spins are 8*8= 64 spins

The possibility that getting 8 twice is only once possible. As it will be only one pair in all the possible values.

Hence, The total probability is 1/64

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Answer:

13

Step-by-step explanation:

1. convert percent into decimal

12.5% = 0.125

2. find the product

0.125 * 104 = 13

The number 13 is 12.5 percent of 104.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

Let x be 12.5% of 104.

Here, 12.5% of 104 =x

x= 12.5/100 ×104 (The word "of" means multiplication)

x= 0.125×104

x= 13

Therefore, 13 is 12.5 percent of 104.

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