Clare used 30% less butter this month than last month when baking holiday treats. If she used 250 tablespoons of butter last month, how many tablespoons did she use this month?

Answer:

The slope is 7/3.

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m = slope.

Answer:

i guess its 80

Step-by-step explanation:

time x thanks man

Answer:the answer is 1)30

Step-by-step explanation:

Answer:

its 2

Step-by-step explanation:

i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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Answer:

  26√11 square inches

Step-by-step explanation:

You want to know the area of a triangle with side lengths 13, 15, and 24 inches.

The area of a triangle can be found using Heron's formula:

  A = √(s(s -a)(s -b)(s -c)) . . . . . where s = (a+b+c)/2

For (a, b, c) = (13, 15, 24), the area is ...

  s = (13 +15 +24)/2 = 26

  A = √(26(26 -13)(26 -15)(26 -24)) = √(26·13·11·2) = 26√11

The area of the triangle is 26√11 square inches.

__

Additional comment

That's about 86.23 square inches.

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Answer:

1805 feet

Step-by-step explanation:

1803-(-2)

1805

Determine the height of television by using the pythagoras theorem.

So height of the television is 10.75 inch.

The situation described can be modeled by a linear function.

In a linear function, the relationship between the variables is constant and can be represented by a straight line on a graph. In this case, as Sarah's visits to the chiropractor increase, her fees decrease by a fixed amount of $5 each time. This means that there is a constant rate of change between the number of visits and the corresponding decrease in fees.

Let's say the number of visits is represented by the variable 'x' and the fees by the variable 'y'. The relationship can be expressed as:

y = mx + b

Where 'm' represents the rate of change (in this case, -5 because the fees decrease by $5) and 'b' represents the initial fee or the y-intercept.

Therefore, the situation of Sarah's fees decreasing by $5 each time she visits the chiropractor can be modeled by a linear function.

The time required for $4300 to become $11,087.70 at a 7% interest rate compounded annually is approximately 12 years.

To determine the time required for an investment to grow from $4300 to $11,087.70 with a 7% annual interest rate compounded annually, we can use the formula for compound interest:

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

Where:

A = Final amount ($11,087.70)

P = Principal amount ($4300)

r = Annual interest rate (7% or 0.07)

n = Number of times interest is compounded per year (1, compounded annually)

t = Time in years (unknown)

Substituting the given values into the formula, we have:

$11,087.70 = $4300(1 + 0.07/1)^(1*t)

Simplifying the equation:

2.58 = (1.07)^t

To solve for t, we can take the logarithm of both sides. Let's take the natural logarithm (ln):

ln(2.58) = ln((1.07)^t)

Using logarithmic properties, we can bring down the exponent:

ln(2.58) = t * ln(1.07)

Now, we can solve for t by dividing both sides by ln(1.07):

t = ln(2.58) / ln(1.07)

Using a calculator, we can evaluate this expression:

t ≈ 11.59 years

Rounded to the nearest year, the time required for $4300 to grow to $11,087.70 at a 7% interest rate compounded annually is approximately 12 years.

Please note that the exact answer is approximately 11.59 years, but rounding to the nearest year gives us 12 years.

The complete question should be:

How long must $4300 be in a bank at 7% compounded annually to become $11,087.70? Round to the nearest year, but CHECK by saving the number on your calculator with all decimal places included. Write your answer in complete sentence form and include correct units.

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Answer:

81

Step-by-step explanation:

The explanation is pretty easy ngl.  You can use the process of elimination but I'll also use math.  It obviously can't be 27 or 9, so it has to be 81 given the 3 possible answers.  Because it's 25 less than 1/3 of the number, you have to add 25 and 2 then multiply the sum to find the answer.  27 times 3 = 81, so that's the answer.  Hope this helps:D

Answer:

81

Step-by-step explanation:

Write the info algebraically:

1/3 of a number = 13x ('of' means times)

25 less = 1/3x - 25

1/3x - 25 = 2

Step 1: Add 25 to both sides

1/3x = 27

Step 2: Divide both sides by 1/3 (or multiply both sides by 3)

x = 27 ÷ 1/3

x = 27 × 3/1

x = 81

Answer = 81

Answer:

12

Step-by-step explanation:

Hope this helps you have a great day!

(a) The power series solution for the Associated Laguerre Equation must terminate because the equation satisfies the necessary termination condition for a polynomial solution.

(b) The general expression for the power series coefficients in terms of the first coefficient can be obtained by using recurrence relations derived from the differential equation.

(a) The power series solution for the Associated Laguerre Equation, when expanded as a polynomial, must terminate because the differential equation is a second-order linear homogeneous differential equation with polynomial coefficients. Such equations have polynomial solutions that terminate after a finite number of terms.

(b) To find the general expression for the power series coefficients in terms of the first coefficient, one can use recurrence relations derived from the differential equation. These recurrence relations relate each coefficient to the preceding coefficients and the first coefficient. By solving these recurrence relations, one can express the coefficients in terms of the first coefficient and obtain a general expression.

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Answer: 3.25 (Add on 0.25 each week)

Step-by-step explanation:

3 + 1/4 = 13/4 = 3 1/4 = 3.25

To find the state matrices X_1, X_2, and X_3, we can use the transition probability matrix P and the initial state matrix X_0.

P = [0.6 0.2 0.1

0.3 0.7 0.1

0.1 0.1 0.8]

X_0 = [0.1 0.2 0.7]

To calculate X_1, we multiply the transition probability matrix P with the initial state matrix X_0:

X_1 = P * X_0

To calculate X_2, we multiply P with X_1:

X_2 = P * X_1

Similarly, to calculate X_3, we multiply P with X_2:

X_3 = P * X_2

Performing these matrix multiplications will give us the state matrices X_1, X_2, and X_3.

Note: Since the provided matrix P has a dimension of 3x3 and the initial state matrix X_0 has a dimension of 1x3, the resulting state matrices X_1, X_2, and X_3 will also have a dimension of 1x3.

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To find the state matrices X₁, X₂, and X₃ given the transition probabilities matrix P and the initial state matrix X₀, we can apply matrix multiplication repeatedly.

P = [0.6 0.2 0.1

0.3 0.7 0.1

0.1 0.1 0.8]

X₀ = [0.1

0.2

0.7]

To find X₁, we multiply P with X₀:

X₁ = P * X₀

To find X₂, we multiply P with X₁:

X₂ = P * X₁ = P * (P * X₀)

To find X₃, we multiply P with X₂:

X₃ = P * X₂ = P * (P * (P * X₀))

Performing the matrix multiplications, we get:

X₁ = [0.6 0.2 0.1] * [0.1

0.2

0.7] = [0.06 + 0.04 + 0.07

0.03 + 0.14 + 0.07

0.01 + 0.02 + 0.56]

X₁ = [0.17

0.24

0.59]

X₂ = [0.6 0.2 0.1] * [0.17

0.24

0.59] = [0.048 + 0.048 + 0.059

0.023 + 0.168 + 0.059

0.007 + 0.048 + 0.472]

X₂ = [0.155

0.25

0.527]

X₃ = [0.6 0.2 0.1] * [0.155

0.25

0.527] = [0.042 + 0.031 + 0.053

0.021 + 0.175 + 0.053

0.006 + 0.05 + 0.422]

X₃ = [0.126

0.249

0.478]

Therefore, the state matrices are:

X₁ = [0.17

0.24

0.59]

X₂ = [0.155

0.25

0.527]

X₃ = [0.126

0.249

0.478]

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Answer:

probably B=-8t+40

Step-by-step explanation:

The expression for the remaining charge in the battery will be B = 40 - 8t.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Lucy left her house in the morning, her cell phone battery was partially charged. Lucy's phone lost battery life at a rate of 8% each hour and 3 hours after leaving her house, the battery had 16% remaining battery life.

The initial battery charge in the phone will be calculated as,

Initial charge = ( 3 x 8%) + 16%

Initial charge = 24% + 16%

Initial charge = 40%

The expression for the remaining charge will be written as,

B = 40 - 8t

Therefore, the expression for the remaining charge in the battery will be B = 40 - 8t.

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The sum of all angles in a triangle = 180 degree

So :

Angle x + Angle 5x + 72 = 180

x + 5x + 72 = 180

6x = 180 - 72

6x = 108

Divide both side by 6 :

6x/6 = 108/6

x = 18

x = 18

since all the angles are less than 90 degree so the triangle is an acute triangle,

as 5x = 90 thus one angle is of 90 degree

Thus triangle is Acute Right angle triangle

Answer : x = 18, acute right angle triangle

Answer:24

Step-by-step explanation:

Answer:

9x5 is 45. Therefore, it would be 60/5 so x would be 12

Step-by-step explanation:

The joint PDF of X and Y is fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

The joint probability density function (PDF) of X and Y can be obtained by multiplying the individual PDFs of X and Y, as they are independent random variables.

Given:

X ~ Exponential(λ), with mean 1 (λ = 1)

Y ~ Uniform(0, X), for 0 < y < x

To find the joint PDF, we first need to express the PDFs of X and Y.

PDF of X:

fX(x) = λ * exp(-λx) for x > 0 (Exponential distribution with parameter λ)

PDF of Y:

fY(y|x) = 1 / x for 0 < y < x (Uniform distribution on interval [0, x])

Now, we can find the joint PDF by multiplying these individual PDFs:

fx.x (x, y) = fX(x) * fY(y|x)

Substituting the PDFs:

fx.x (x, y) = (λ * exp(-λx)) * (1 / x)

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x

Therefore, the fully specified joint PDF of X and Y is:

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

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Answer:

4/5 or .8

Step-by-step explanation:

To maximize the harvest, we need to find the number of trees per acre that yields the highest total bushels of fruit.

Let's assume the number of additional trees planted per acre beyond 95 is 'x'. For each additional tree planted, the yield of each tree decreases by 2 bushels. Therefore, the yield of each tree can be expressed as (30 - 2x) bushels.

If the farmer plants 95 trees per acre, the total yield of fruit can be calculated as follows:

Total yield = Number of trees per acre * Yield per tree

= 95 trees * 30 bushels/tree

= 2850 bushels

If the farmer plants 'x' additional trees per acre, the total yield can be calculated as:

Total yield = (95 + x) trees * (30 - 2x) bushels/tree

To find the value of 'x' that maximizes the total yield, we can create a function and find its maximum. Let's define the function 'Y' as the total yield:

Y = (95 + x) * (30 - 2x)

Expanding the equation:

Y = 2850 + 30x - 190x - 2x^2

Y = -2x^2 - 160x + 2850

To find the maximum value of 'Y', we can take the derivative of 'Y' with respect to 'x' and set it equal to zero:

dY/dx = -4x - 160 = 0

Solving this equation gives us:

-4x = 160

x = -160/4

x = -40

Since the number of trees cannot be negative, we discard the negative value. Therefore, the farmer should not plant any additional trees beyond the initial 95 trees per acre to maximize her harvest.

So, the number of trees she should plant per acre to maximize her harvest is 95 trees.

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Answer:

the present age of the father be x and the present age of the son be y.

It is given that man is 24 years older than his son that is:

x=y+24

x−y=24..........(1)

Also, 12 years ago, he was five times as old as his son that is:

(x−12)=5(y−12)

x−12=5y−60

x−5y=−60+12

x−5y=−48..........(2)

Now subtract equation 1 from equation 2 to eliminate x, because the coefficients of x are same. So, we get

(x−x)+(−5y+y)=−24−48

i.e. −4y=−72

i.e. y=18

Substituting this value of y in (1), we get

x−18=24

i.e. x=24+18=42

Hence, the present age of the father is 42 years and the present age of the son is 18 years.

Step-by-step explanation:

Answer:

(a) 1:12

(b) 12:1

(c) 1:100

(d) 100:1

A variation can be direct, inverse or joint

The function of the variation is \(tw = 4/5\), and the value of t when w = 9 is 4/45

Given that w and t vary inversely, then it means that:

tw = k

Where, k is the constant of variation

t = 1/5 when w = 4.

So, we have:

\(1/5 * 4 = k\)

This gives

\(4/5 = k\)

Rewrite as:

\(k = 4/5\)

Recall that:

tw = k

So, we have:

\(tw = 4/5\)

When w = 9, the equation becomes

9t = 4/5

Divide both sides by 9

\(t = 4/45\)

Hence, the function of the variation is \(tw = 4/5\), and the value of t when w = 9 is 4/45

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Answer:

The missing number of the unit rate is 4

Step-by-step explanation:

20 divided by 5 is 4, which is the same thing as \(\frac{4}{1}\), so the missing number of the unit rate is 4.

Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

Answer:

1

Step-by-step explanation:

The length of the tree house with a base of 7 ft on the model is given as follows:

1/3 ft.

The length of the model is obtained applying the proportions in the context of the problem.

The scale is a ratio that relates the size of a drawing or map to the actual size of the object or area being represented. It indicates how much the drawing or map has been reduced or enlarged in size from the actual object or area.

Hence the scale of 1:21 means that each ft on the drawing represents 21 ft of actual distance, hence the length of the drawing for an actual distance of 7 ft is given as follows:

1/21 x 7 = 1/3 ft.

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