What does 5 less than 3 times mean? I need help badly it’s due tomorrow for Algebra 1.

HERES THE FULL QUESTION: The width of a rectangle is five less than three times the length of the rectangle if the perimeter of the rectangle is 70 inches what are the dimensions of the rectangle?

Step-by-step explanation:

bag contains 50 coins

To find :

Total amount of the coins bag contains.

Solution:

According to the given statement, a bag contains 50 coins.

Number of pennies = 12% of 50

                                = 0.12 × 50

                                = 6 pennies

Number of dimes  = 40% of 50

                              = 0.40 × 50

                              = 20 dimes

Number of nickles = 8 more than pennies

                               = 8 + 6

                              = 14 nickles

Number of quarters = Rest of the coins

                                = 50 -(6 + 20 + 14)

                                = 50 - 40

                               = 10 quarters

Since,

1 penny = 0.01 dollar

6 pennies = 0.01 × 6 = 0.06 dollar

1 dime = 0.10 dollar

20 dimes = 0.10 × 20 = 2.00 dollar

1 nickel = 0.05 dollar

14 nickel = 0.05 × 14 = 0.70 dollar

1 quarter = 0.25 dollar

10 quarter = 0.25 × 10 = 2.50 dollars

Total value of the coins in the bag = 0.06 + 2.00 + 0.70 + 2.50

                                                         = 5.26 dollars

The bag contains 5.26 dollars

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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Ans: x°= 48°

pa brainliest po thanks

Answer:

Step-by-step explanation:

ABC = 180° - 114° = 66°

x = 180 - 66 - 66 = 48°

Answer:

4

Step-by-step explanation:

x²+8x+11=0

x²+8x+(+4)²-(+4)²+11=0

Answer:

16

Step-by-step explanation:

x2+8x=  −11−11

28​=4→(4)2=16

x2+8x+16=x2+8x+16=  −11+16−11+16

(x+4)2=  55

16

Answer:

15l

Step-by-step explanation:

There are 5 8sq m in 40sq m

total paint is 5*3=15

Answer:

10x+8

Step-by-step explanation:

4( x + 2) + 6x

Distribute

4x+8 +6x

Combine like terms

10x+8

Answer:

10x+8

Step-by-step explanation:

4x+8+6x

(4x+6x)+8

10x+8

The length of the diagonal of a square with a perimeter of 56 is 14√2.

A diagonal is the longest line that divides a plane shape into two equal parts.

To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.

Formula:

Where:

From the question,

Given:

Substitute the value into equation 1 and solve for a

Finally to find the length of the diagonal of the square, we use the formula below

Where:

Substitute into equation 2

Hence, the length of the diagonal is 14√2.

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Answer:

qfewwqeffwqfefewqwqreg

Step-by-step explanation:

Answer:

where is the graph

Step-by-step explanation:

The standard form is 6\(x^4\) + 10x³ - 4x² - 15x + 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(3x−1) (2x³ +4x² −5)

Simplifying

3x (2x³ +4x² −5) - 1 (2x³ +4x² −5)

6\(x^4\) + 12x³ - 15x - 2x³ - 4x² + 5

Adding the like terms.

6\(x^4\) + 10x³ - 4x² - 15x + 5

Thus,

6\(x^4\) + 10x³ - 4x² - 15x + 5

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The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Let P and Q be two complex numbers such that

P = a+bi

Q = c+di

Where a,b,c,d are real numbers and i = sqrt(-1).

This means i^2 = -1.

-------------------

Adding P and Q means

P+Q = (a+bi)+(c+di)

P+Q = a+bi + c+di

P+Q = (a+c) + (bi+di)

P+Q = (a+c) + (b+d)i

As you can see, we just add the corresponding components together.

-------------------

Subtraction is a similar story.

P-Q = (a+bi)-(c+di)

P-Q = a+bi - c-di

P-Q = (a-c) + (bi-di)

P-Q = (a-c) + (b-d)i

We subtract the corresponding components

-------------------

Multiplication is a bit more complicated.

We'll use the FOIL rule

P*Q = (a+bi)*(c+di)

P*Q = a*c + a*di + bi*c + bi*di

P*Q = a*c + ad*i + bc*i + bd*i^2

P*Q = a*c + ad*i + bc*i + bd*(-1)

P*Q = a*c + ad*i + bc*i - bd

P*Q = (ac - bd) + (ad*i + bc*i)

P*Q = (ac - bd) + (ad + bc)i

Unfortunately multiplication isn't as simple as addition or subtraction, but we can at least make a tidy formula for it. You could also use the box method to visually organize the terms into a table to help multiply out P and Q.

Answer:

because they have different stepa

Answer: 8,000,000

Step-by-step explanation:

10 to the power of 6 means = 10×10×10×10×10×10 . 106 should give you 1,000,000. Therefore 8 × 1,000,000 should give you 8,000,000.

The probability distribution of the number of customers that enter the store on a given day is described as follows:

Poisson with a mean of 70 customers.

In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:

Hence the mean is of:

8 + 16 + 18 + 28 = 70 customers.

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Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

Answer:

9000

Step-by-step explanation:

I did 15000 divided by 10 x 6

Hope this helped!

The augmented matrix corresponding to the system of equations in this problem is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

The first row is constructed according to the coefficients of the first equation, hence it is given as follows:

[-6 -5 -4 7].

The second row is constructed according to the coefficients of the second equation, hence it is given as follows:

[7 -9 -1 -7].

The third row is constructed according to the coefficients of the third equation, hence it is given as follows:

[-9 -3 -6 7].

Hence the matrix is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

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Answer:

It would be 3 meters apart

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

The range for the given domain is:

{-18, -6, 6}

Here we have the function:

p = 4q - 6

And we want to find the range for the domain  { -3, 0, 3}

To get it, just evaluate the function in the given values.

When q = -3

p = 4*-3 - 6 = -18

When q = 0

p = 4*0 -6 = -6

When q = 3

p = 4*3 - 6 = 6

The range is {-18, -6, 6}

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Answer:

17.1%

Step-by-step explanation:

To find the percentage of oak trees in the wood, divide the number of oak trees by the total number of trees (sum of all tree types), and then multiply by 100 to express it as a percentage:

\(\begin{aligned}\textsf{Percentage of oak trees}&= \dfrac{\textsf{Number of oak trees}}{\textsf{Total number of trees}} \times 100\\\\&= \dfrac{130}{420+130+210} \times 100\\\\&= \dfrac{130}{760} \times 100\\\\&=0.171052631... \times 100\\\\&=17.1\%\; \sf (1\;d.p.)\end{aligned}\)

Therefore, approximately 17.1% of the trees in the wood are oak trees.

Answer:

17.1%

Step-by-step explanation:

In order to calculate the percentage of trees that are oak trees, we can use the following formula:

\(\textsf{Percentage of oak trees }=\dfrac{\textsf{ Number of oak trees }}{\textsf{total number of trees} }\cdot 100\% \)

We know that the number of oak trees is 130 and the total number of trees is 420 + 130 + 210 = 760.

Substituting these values into the formula, we get:

\(\textsf{Percentage of oak trees }=\dfrac{130}{760}\cdot 100\% \\\\ = 0.1710 \cdot 100\% \\\\ \approx 17.1 \% \textsf{( in 1 d.p.)}\)

Therefore, 17.1% of the trees in the wood are oak trees.

Answer:

1/2

Step-by-step explanation:.

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

t = b + n

Step-by-step explanation:

for the 2 lines to be parallel then their slopes must be equal

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (x₁, a + n ) and (x₂, y₂ ) = (x₂, t ) ← 2 points on line k

m = \(\frac{t-(a+n)}{x_{2}-x_{1} }\) = \(\frac{t-a-n}{x_{2}-x_{1} }\)

repeat with

(x₁, y₁ ) = (x₁, a ) and (x₂, y₂ ) = (x₂, b ) ← 2 points on line j

m = \(\frac{b-a}{x_{2}-x_{1} }\)

equating the 2 slopes gives

\(\frac{t-a-n}{x_{2}-x_{1} }\) = \(\frac{b-a}{x_{2}-x_{1} }\)

since the denominators are the same on both sides, then equate the numerators

t - a - n = b - a ( add a to both sides )

t - n = b ( add n to both sides )

t = b + n

Answer:

1 5/32 is equal to 1.15625 in decimal form.

Step-by-step explanation:

Hope this helped, Have a Great Day!!

1 and 5/32 is equivalent to 1.15625 as a decimal.

To convert the mixed number 1 and 5/32 to a decimal, you need to combine the whole number and the fractional part.

First, you convert the fractional part to a decimal.

The denominator of 32 tells you that there are 32 equal parts in a whole.

To determine the value of 5/32, you divide the numerator (5) by the denominator (32):

5 ÷ 32 = 0.15625

Next, you add the decimal value of the fractional part (0.15625) to the whole number (1):

1 + 0.15625 = 1.15625

Therefore, 1 and 5/32 is equivalent to 1.15625 as a decimal.

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The Value of x is 2/3.

The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.

The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.

Mean = (x + x+3 + x-5 + 2x + 3x) / 5

Next, we simplify the expression:

Mean = (5x - 2 + 3x) / 5

Mean = (8x - 2) / 5

We are given that the mean is also equal to x:

Mean = x

Setting these two expressions equal to each other, we have:

(x) = (8x - 2) / 5

To solve for x, we can cross-multiply:

5x = 8x - 2

Bringing all the x terms to one side of the equation and the constant terms to the other side:

5x - 8x = -2

-3x = -2

Dividing both sides by -3:

x = -2 / -3

Simplifying, we get:

x = 2/3

Therefore, the value of x is 2/3.

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Answer:

a

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

b

  \(P(A) =  \frac{1}{8}\)

c

 \(P(B) = \frac{1}{4}\)

d

\(P(C) = \frac{5}{16}\)

Step-by-step explanation:

From the question we are told that

The number of True - False question is n = 4

The number of answers recorded are k = 4

Generally the outcomes in the sample space are 16 and they are listed below

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

Generally from the list of the possible outcome we see that the number of outcome where the answers are the same is 2 i.e [TTTT] and [FFFF]

So the probability that all the answers are the same is mathematically represented as

\(P(A) = \frac{2}{16}\)

=> \(P(A) = \frac{1}{8}\)

Generally from the list of the possible outcome we see that the number of outcome where exactly one answer is true is 4 i.e [FFTF] , [FFFT],[TFFF] , [FTFF]

So the probability that exactly one of the four answers is "True." is mathematically represented as

\(P(B) = \frac{4}{16}\)

=> \(P(B) = \frac{1}{4}\)

Generally from the list of the possible outcome we see that the number of outcome where at most one of the four answers is true is 5 i.e [FTFF] , [FFFF] , [FFTF] , [FFFT] ,[TFFF]

So the probability that at most one of the four answers is mathematically represented as

\(P(C) = \frac{5}{16}\)

The probabilities of all same, exactly one true, and most one of the four are true is 0.125, 0.25, and 0.3125 respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A section of an exam contains four True-False questions.

A completed exam paper is selected at random, and the four answers are recorded.

Total event = 16

A.  The sample space will be shown in the table below.

\(\rm Sample \ space = 16 \ \begin{Bmatrix}FFFF & FFFT & FFTF & FFTT \\FTFF & FTFT & FTTF & FTTT \\TFFF & TFFT & TFTF & TFTT \\TTFF & TTFT & TTTF & TTTT\end{Bmatrix}\)

B.  The probability that all the answers are the same will be.

Favorable event = 2 ={(TTTT, FFFF}

Then we have the probability,

\(\rm P(B) =\dfrac{2}{16} =\dfrac{1}{8} = 0.125\)

C.  The probability that exactly one of the four answers is "True".

Favorable event = 4 {(FFFT, FFTF, FTFF, TFFF}

Then we have the probability,

\(\rm P(C) =\dfrac{4}{16} =\dfrac{1}{4} = 0.25\)

D.  The probability that at most one of the four answers is "True".

Favorable event = 5 {(FFFF, FFFT, FFTF, FTFF, TFFF}

Then we have the probability,

\(\rm P(D) =\dfrac{5}{16} =0.3125\)

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Problem 2.

Using the unit circle as our guide,

Point A would be at 0 degrees

There are 12 points on the circle

Take 360 degrees and divide by 12

360/12 = 30

Each pie shaped wedge is 30 degrees

C is 2 pie pieces so it is 2*30 or 60 degrees from point A

H is 8 pie shapes wedges so it is 8*30 or 240 degrees from point A

Looking at the diagram we can see that A and G are the same distance from the ground

B and F are the same distance from the ground

C and E are the same distance from the ground

H and L are the same distance from the ground

I and K are the same distance from the ground

Answer:

there are two operation end modes [ = , < ]

so, it remains an expression

Step-by-step explanation:

let the number be x :

\( \{(n + 3) = 6 \} < 2n\)

The solution of the written expression, ''The sum of a number and 3 is 6 less than twice that number'' is 9.

Here,

The written expression, ''The sum of a number and 3 is 6 less than twice that number''.

We have to solve this expression.

What is Mathematical expression?

An expression consists of one or more numbers or variables along with one more operation.

Now,

Let a number is x.

By the given written expression, we can write the mathematical expression as,

x + 3 = 2x - 6

By solving;

x + 3 = 2x - 6

3 + 6 = 2x - x

9 = x

x = 9

Hence, the value of written expression is x.

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