Today, Reza ate 20 grapes, which was 400% as many
grapes as he ate yesterday. Explain how to use
equivalent ratios to find the number of grapes Reza ate
yesterday. (help plz)

Answer:

$75

Step-by-step explanation:

15x5=$75

The amount of money Mary has left in her account is $ 45

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount of money in Mary's account be = $ 120

The amount of money that gets deducted for each week = $ 5

Total number of weeks elapsed = 15 weeks

So , the equation will be

Total amount deducted after 15 weeks = number of weeks elapsed x amount of money that gets deducted for each week

Total amount deducted after 15 weeks = 15 x 5

                                                                 = $ 75

Therefore , the equation will be

The amount left in Mary's account = total amount of money in Mary's account - Total amount deducted after 15 weeks

The amount left in Mary's account = 120 - 75

                                                         = $ 45

Hence , The amount of money Mary has left in her account is $ 45

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Answer:

2.05m

Step-by-step explanation:

Therefοre, the number οf sunny days is 96.

An equatiοn is a mathematical statement that asserts the equality οf twο expressiοns. It typically cοnsists οf variables, cοnstants, and mathematical οperatiοns, such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts.

A mathematical assertiοn οf the equality οf twο expressiοns is knοwn as an equatiοn. Variables, cοnstants, and mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rects are generally included.

Given by the questiοn.

Let "x" be the number οf sunny days οver the last 96 days.

If it was sunny until thοse days, that means all 96 days were sunny.

We can set up the equatiοn:

x = 96

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Answer:

iek

Step-by-step explanation:3283349

The external finance needed=$33,689

PRO FORMA INCOME STATEMENT

15%Growth

20%

25%

Sales

$ 1,127,874

$ 1,176,912

$ 1,225,950

Costs

$ 911,904

$ 951,552

$ 991,200

Other expenses

$ 23,069

$ 24,072

$ 25,075

EBIT

$ 192,901

$ 201,288

$ 209,675

Interest Paid

$14,740

$14,740

$14,740

Taxable Income

$ 178,161

$ 186,548

$ 194,935

Taxes(21%)

$ 37,414

$ 39,175

$ 40,936

Net Income

$ 140,747

$ 147,373

$ 153,999

Dividend

$ 45,705

$ 47,856

$ 50,008

Added to RE

$ 95,042

$ 99,517

$ 103,991

EFN FOR 15% SALES GROWTH

(A).Required increase in assets=(Current total asset)* (percentage increase in sales)

The required increase in assets=622440*0.15= $93,366

(B).Spontaneous increase in liabilities=(accounts payable)* (percentage increase in sales)=71720*0.15= $ 10,758

(C)Increase in retained earning =$95,042 (From Pro Forma income statement )

External Finance Required=(A)-(B)-(C)=$93366-$10758-$95042= $ (12434)

A

Total assets increase

$ 93,366

B

Increase in accounts payable

$ 10,758

C

Added to retained Earnings

$95,042

D=A-B-C

ExternalFinance Needed(EFN)

$ (12,434)

No External Finance is needed . Retained earning will provide the necessary capital>

EFN FOR 20% SALES GROWTH

(A).Required increase in assets=(Current total asset)* (percentage increase in sales)

Required increase in assets=622440*0.20= $ 124,488

(B).Spontaneous increase in liabilities=(accounts payable)* (percentage increase in sales)=71720*0.20= $14,344

(C)Increase in retained earning =$99517(From Pro Forma income statement )

External Finance Required=(A)-(B)-(C)=$124488-$14344-$99517= $ 10627

A

Total assets increase

$ 124,488

B

Increase in accounts payable

$ 14,344

C

Added to retained Earnings

$99,517

D=A-B-C

ExternalFinance Needed(EFN)

$ 10,627

External Finance Needed=$10,627

EFN FOR 25% SALES GROWTH

(A).Required increase in assets=(Current total asset)* (percentage increase in sales)

Required increase in assets=622440*0.25= $ 155,610

(B).Spontaneous increase in liabilities=(accounts payable)* (percentage increase in sales)=71720*0.25= $ 17,930

(C)Increase in retained earning =$103,991(From Pro Forma income statement )

External Finance Required=(A)-(B)-(C)=$155610-$17930-$103991= $ 33,689

A

Total assets increase

$ 155,610

B

Increase in accounts payable

$ 17,930

C

Added to retained Earnings

$103,991

D=A-B-C

ExternalFinance Needed(EFN)

$ 33,689

External finance needed=$33,689

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The greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

The slope of a straight line is the measure of the tangent of the angle that the line makes with the + x axis. The intercept of a straight line is -

y = mx + c

from this we can write slope [m] as -

mx = y - c

m = (y - c)/x

If y - intercept [c] is zero, then -

m = y/x

Given is a equation, tabular data and a graph representing a straight line

Slope of a line also tells us about the rate of change of [y] value with respect to the [x] value.

[A]

For the equation -

D = 55t

The slope will be [m] = 55.

[B]

For the tabular data, take two coordinates -

(1, 475) and (2, 535)

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

The slope will be -

[m] = (535 - 475)/(2 - 1)

[m] = 60

[C]

For the graph we have a straight line that passes through the coordinates as follows -

(0, 100)

(1, 150)    

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (150 - 100)/(1 - 0)

[m] = 50

The slope of the line is maximum for the tabular data [B].

Therefore, the greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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Step-by-step explanation:

I think the problem definition degraded a bit, when you transferred it over to here.

so, let me try to rephrase this properly, and I hope that my interpretation fits the original problem.

the base of a 3-sided prism is an isoceles triangle with a baseline length of 80 cm, and a side length of 41 cm.

calculate the surface area of the prism, if the length of the height of the prism is equal to the height of the base triangle to its baseline.

let's go through this step by step (even the ones you skipped) :

first : isoceles means that both legs are equally long. so, the prism base is a 80 - 41 - 41 triangle.

the height to its baseline is therefore splitting the baseline in the middle (into 2 equal parts) : 2×40 cm.

therefore it is also splitting the whole main triangle into 2 equal right-angled triangles (half of the baseline, a leg of the main triangle, and the height of the main triangle to the baseline).

now that we have right-angled triangles, we can use Pythagoras to calculate the height, as the leg of the main triangle is now the baseline of the "half" right-angled triangle :

41² = 40² + height²

1681 = 1600 + height²

81 = height²

height = 9 cm

so, the height to the baseline of the main triangle is 9 cm, and so is per definition the height of the prism.

that means, no, you were not correct. I honestly don't know what you did there at the beginning with the height calculation.

but let's continue.

so, the base and the top of the prism are such equal isoceles triangles.

the sides of the prism are (3) rectangles :

one is 80×9 cm²

and the other two are 41×9 cm² each

the area of a triangle is

baseline × height / 2

in our case

80 × 9 / 2 = 40 × 9 = 360 cm²

we have 2 such triangles (base and top) :

2 × 360 = 720 cm²

the areas of the rectangles are

80 × 9 = 720 cm²

41 × 9 × 2 = 738 cm²

so, the total surface area of the prism is

720 + 720 + 738 = 2178 cm²

FYI

if you were looking for the volume of the prism, that would be

base area × prism height = 360 × 9 = 3240 cm³

Since the determinant of matrix A is nonzero (17 ≠ 0), we conclude that the polynomials p1(x), p2(x), and p3(x) are linearly independent.

Suppose we have a set of polynomials P = {p1(x), p2(x), p3(x)} where:

p1(x) = 2x^2 - x + 1

p2(x) = 3x^2 + 2x - 1

p3(x) = 4x^2 + 3x + 2

To test the linear independence of these polynomials, we can create coordinate vectors for each polynomial by listing their coefficients. Let's represent each polynomial as a vector in the vector space V = R^3 (3-dimensional real vector space).

The coordinate vectors for the polynomials p1(x), p2(x), and p3(x) are:

v1 = [2, -1, 1]

v2 = [3, 2, -1]

v3 = [4, 3, 2]

Now, to determine the linear independence of these polynomials, we need to check if the vectors v1, v2, and v3 are linearly independent. This can be done by forming a matrix using these vectors and performing a row-reduction or determinant calculation.

Create a matrix A using the coordinate vectors as rows:

A = | 2 -1 1 |

| 3 2 -1 |

| 4 3 2 |

Perform row operations to reduce the matrix to its row-echelon form or calculate the determinant. If the determinant of the matrix is nonzero, then the polynomials are linearly independent.

Let's calculate the determinant of matrix A to determine the linear independence of the polynomials:

det(A) = 2(22 - (-1)(3)) - (-1)(32 - (-1)(4)) + 1(3*3 - 2(4))

= 2(4 + 3) - (-1)(6 - 4) + 1(9 - 8)

= 2(7) - (-1)(2) + 1(1)

= 14 + 2 + 1

= 17

Since the determinant of matrix A is nonzero (17 ≠ 0), we conclude that the polynomials p1(x), p2(x), and p3(x) are linearly independent.

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Answer:

60 feet of wood :)

Step-by-step explanation:

I looked it up

Answer:

60 feet of wood

Answer:

What do you mean? I can help i just need nore info

After the first half hour, the bacteria would double to 1000.

After the second half hour, it would double again to 2000.

After the third half hour, it would double again to 4000.

So, after 2 hours (which is 4 half hours), there would be 16 times the original amount of bacteria, or 500 x 2^4 = 8000 bacteria.

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Answer:

The correct option is A,3875  passengers

Step-by-step explanation:

The curve of best fit for the date y=-5x^2+60x+3715

For April which month 4  which means that x is 4

By substituting 4 for x in the equation we can determine y, the number of passengers that arrived on flights at the airport  is determined thus.

y=-5*4^2+(60*4)+3715

y=-5*16+240+3715

y=-80+240+3715=3875

The number of passengers that arrived by flights in April, month 4 is 3875

Answer:

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore, given as follows;

\(f(x) = 64 \times \left(\dfrac{3}{4} \right) ^{(x - 1)}\)

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore the correct answer is C

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

x = 12

Step-by-step explanation:

Exterior angles thm:

8x - 10 + 5x - 12 = 134

13x - 22 = 134

13x = 134 + 22

13x = 156

x = 12

Answer:

f(-8) = -2

Step-by-step explanation:

The equation of the function is given as;

F(x) = x/4

To get F(-8), we simply substitute-8 for x

Thus we have

F(-8) = -8/4 = -2

Answer:

f(-8) = -2

Step-by-step explanation:

took the test on edge

The range of g(x) is [-30, -7].Thus, we have the following results:Domain of g(x) = [-5, 20]

Range of g(x) = [-30, -7]

Given that the function y = f(x) has domain D = [-7, 18] and range R = [-19, 4] and f(-7) = -19 and f(18) = 4. We have to find the domain D and range R of the new function,  g(x) = f(x - 2) - 11.We know that the domain of a function f(x) is the set of all real values of x for which the function is defined or gives a real value. Let us find the domain of g(x):Domain of g(x):The function g(x) is obtained by replacing x with x - 2 in the function f(x). Hence, we need to add 2 to the end points of the domain of f(x) to obtain the domain of g(x). Therefore, the domain of g(x) is D = [-7 + 2, 18 + 2] = [-5, 20]. Hence, the domain of g(x) is [-5, 20].We know that the range of a function f(x) is the set of all real values that the function takes. Let us find the range of g(x):Range of g(x):The range of g(x) is obtained by shifting the range of f(x) down by 11 units. Therefore, the range of g(x) is R = [-19 - 11, 4 - 11] = [-30, -7]. Hence, the range of g(x) is [-30, -7].Thus, we have the following results:Domain of g(x) = [-5, 20]Range of g(x) = [-30, -7]

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Therefore , the solution of the given problem of equation comes out to be  y = 23.78t - 5t²

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,
Given :parametric equation

x be the speed of water

t be the time

v be the speed of dolphin

=> x = (vcosx)t +x₀

=> v = 32

=> x = 48

=> x = (32 X cos 48)t + 0

=> x = 21.41t

thus,

=>  y = (vsintx)t - 1/2gt² + y₀

=>   y₀ = 0

=>  v = 32

=> x = 48

=> g = 10

=> y = (32sin48)t -1/2 *10*t² +0

=>  y = 23.78t - 5t²

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Answer:

Value: 10

Step-by-step explanation:

1. Let us first write down the expression, changing it a bit to our convenience: 2(x - 3) + 2x - 4

2. Substitute this value of x into the expression as such:

2(5 - 3) + 2(5) - 4

3. Now we can approach this first part of the problem in two ways:

Option 1. distribute the 2 to the 5 and then the -3, in 2(5 - 3)

Option 2. subtract 3 from 5, then multiply 2 by that value

4. Given such, let us try the 2nd option for simplicity, and carry on with our calculations: 2(2) + 2(5) - 4

5. Now apply algebra and solve this expression:

2(2) + 2(5) - 4 = 4 + 10 - 4 = 14 - 4 = 10

Answer:

B

Step-by-step explanation:

You count the gradient of the line

All od the gradient is 5 jut b is 55

Thus b is different from the others

Answer:

If you need anything just let me know.

Step-by-step explanation:

Hope you have a good day.

Answer:

x = 39

Step-by-step explanation:

The square on the angle means that angle is 90 degrees, also known as a right angle. A triangle is 180 degrees so all the sides added together is 180:

51 + 90 + x = 180

141 + x = 180

x = 39

Answer:

20%

Step-by-step explanation:

Answer:

  9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

__

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

  Tan = Opposite/Adjacent

Using the given values, we have ...

  tan(24°) = AC/AB = (tree height)/(distance from tree)

  tan(24°) = AC/(22 m)

Multiplying by 22 m gives ...

  tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

a.) the decimal equivalent of (10000)7 is 2401, 1715 is the highest number that can be represented with four digits in base 7.

(A) In order to change a number from base 7 to base 10, we must multiply each digit by the relevant power of 7 before adding the results. The single non-zero digit in the number (10000)7 is in the leftmost (most important) position. This numeral is 1, and the power of 7 it corresponds to is 74. As a result, we have:

(10000)7 = 1 × 7^4 = 1 × 2401 = 2401

Hence, the decimal equivalent of (10000)7 is 2401.

(b) As 6 is the largest digit in base 7, the largest number that can be represented with four digits in base 7 contains the digits 6666. It is represented by the decimal:

6666(base 7) = 6×7^3 + 6×7^2 + 6×7^1 + 6×7^0 = 1715

Hence, 6666 (base 7) or 1715 is the highest number that can be represented with four digits in base 7. (base 10).

(c) While the greatest number that can be expressed with four digits in base 7 has all digits equal to 6, the number (10000)7 only has one non-zero digit in the leftmost position. The numbers in both situations have the same amount of digits, but their values differ greatly. In base 7, (10000)7 is the smallest conceivable 5-digit number, whereas 6666 (base 7) is the greatest possible 4-digit number. These two numbers are related because of this.

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Timothy is currently 7 years old and Adele's current age is 12 years old.

To solve this age problem involving Adele and Timothy, we can set up two equations based on the information given. Let A represent Adele's current age and T represent Timothy's current age. The problem states:
Adele is 5 years older than Timothy: A = T + 5
In three years, Timothy will be 2/3 of Adele's age: (T + 3) = (2/3)(A + 3)
First, let's rewrite equation 1 in terms of T: T = A - 5
Now, substitute this expression for T into equation 2:
(A - 5 + 3) = (2/3)(A + 3)
Simplify the equation:
A - 2 = (2/3)(A + 3)
Multiply both sides by 3 to eliminate the fraction:
3(A - 2) = 2(A + 3)
Expand:
3A - 6 = 2A + 6
Now, solve for A:
A = 12
So, Adele's current age is 12 years old. To find Timothy's age, we can use the equation T = A - 5:
T = 12 - 5 = 7
Thus, Timothy is currently 7 years old. Therefore, the correct answer is not among the given options, as Adele's current age is 12 years.

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