Solve:

-7/2 + (-5 1/2) + 8 3/4

Answer:

100

Step-by-step explanation:

Original price: x

x + (7%*x) = 107.

107 is 107% of the original price

107 = 1.07x

Divide by 1.07 on both sides

x = 100

Check:

7% of 100 is 7

100 + 7 = 107

Hope this helps :)

This is an arithmetic sequence with a common difference given by d= -7

I will start by defining my first term as u⁰=361

Now we have to think, if u⁰ is my 1st term than my 47th term would be u⁴⁶ not u⁴⁷ since i start counting from 0 and not 1.

Using the relation that describes the implicit relation of an arithmetic sequence, i can say:

u(n)=u⁰+nd where n is any number

u⁴⁶=u⁰+46d

u⁴⁶=361+46(-7)

u⁴⁶=361-322

u⁴⁶=39

Answer:

39.

Step-by-step explanation:

This is an arithmetic sequence with common difference -7

47th term = a + d(n - 1)

= 361  - 7(47-1)

= 39.

The answer here is 24

According to the question

The pattern of the given numbers is that each number is 2 less than the previous number.

So the next number in the sequence is 26 - 2 = 24.

So subtracting 2 from 30, 28 and 26 gives the sequence 28, 26 and 24.

What is a pattern?

A pattern is a repeated sequence of elements that follow a certain rule or formula, which can help us make predictions and solve problems.

What is a sequence?

A sequence is a collection of numbers, shapes, or other objects arranged in a specific order or pattern, which can be finite or infinite and may follow a certain rule or formula.

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The sequence of numbers obtained after subtracting 2 is 28, 26, 24.

A sequence is a collection of numbers, shapes, or other objects arranged in a specific order or pattern, which can be finite or infinite and may follow a certain rule or formula.

In the given sequence of numbers, we are asked to subtract 2 from each of the numbers. To do this, we simply subtract 2 from the first number, which gives us the second number in the sequence. Then we subtract 2 from the second number to get the third number, and so on.

So, starting with the first number 30, we subtract 2 from it to get the second number 28. Then we subtract 2 from 28 to get 26, and finally, we subtract 2 from 26 to get 24.

Therefore, the sequence of numbers obtained after subtracting 2 from each of the given numbers is 28, 26, 24.

Subtracting 2 from each of the given numbers, we get:

30 - 2 = 28

28 - 2 = 26

26 - 2 = 24

Therefore, the sequence of numbers obtained after subtracting 2 is 28, 26, 24.

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Answer:

1920 cubes.

Step-by-step explanation

Turn both the mix numbers into improper fractions.

2 2/5 = 12/5

3 1/5 = 16/5

Then you will turn 1/5 into its reciprocal and multiply both the improper fractions by it. You can just casually multiply 2 and 5.

12/5 * 5/1 = 12

16/5 * 5/1 = 16

2 * 5 = 10

Next you multiply all together to get 1920 cubes.

(I could be missing a step. I apologize if I did.)

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

1. y = 2x + 7

Step-by-step explanation:

The equation of a linear function is y = mx + b. The "x" has to be a first-degree polynomial (no exponents).

The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.

The five-sided figure is a trapezoid with two parallel sides, so we can use the formula for the area of a trapezoid to find the total area.

Area of a trapezoid = (sum of the lengths of the two parallel sides) / 2 * height

Let's call the length of the longer parallel side "L". Then the height of the figure is 22 feet, and the length of the shorter parallel side is 16 feet.

Area = (L + 16) / 2 * 22

We also know that the portion from the vertex to the perpendicular height is 8 feet, and the portion from a point to a vertical line created by two vertices is 4 feet. These two lengths form a right triangle, so we can use the Pythagorean theorem to find the length of the longer parallel side, L.

L² = (8 + 4)² = 64

L = 8

Now we can use the formula for the area of a trapezoid to find the total area.

Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528

The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.

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the regular price is "x", which of course is the 100%, but we also know that $459 is 32% off that, hmmmmm well 100% - 32% = 68%, so $459 is really 68% of "x", because $459 is whatever "x" is minus 32%.

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 459&68 \end{array}\implies \cfrac{x}{459}=\cfrac{100}{68}\implies \cfrac{x}{459}=\cfrac{25}{17} \\\\\\ 17x = 11475\implies x = \cfrac{11475}{17}\implies x = 675\)

The solution to the equation -4(4x + 9) = -2(8x + 18) is defined as follows:

C. Infinite real solutions.

The solution to the equation 3(5x + 9) = 4(6x + 10) is defined as follows:

C. Exactly one real solution at x = 1 and 4/9.

The first equation is defined as follows:

-4(4x + 9) = -2(8x + 18).

Applying the distributive property, we have that:

-16x - 36 = -16x - 36

The two sides of the equality are equal, hence there is an infinite number of solutions.

The second equation is given as follows:

3(5x + 9) = 4(6x + 10)

Applying the distributive property, we have that:

15x + 27 = 24x + 40

9x = 13

x = 13/9

x = 1 and 4/9.

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Answer:

hsad

Step-by-step explanation:

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents

The given parameters are

Principal, P = 1287

Rate, R= 4%

Time, T = 8

The balance in dollars and cents in Larry's savings account at the end of these 8 years

Balance = P * PRT

This gives

Balance = 1287 + 1287 * 4% * 8

Evaluate

Balance = 1698.84

Hence, the balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents

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Answer:

f(x) has a greater slope.

Step-by-step explanation:

The slope of the image line

= difference in y coordinates / difference in x coordinates

= (7-3) / (3-2)

= 4.

The  slope of f(x) = 6x + 1 is  6.

The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

What is mean by straight line?

A straight line is a combination of endless points joined on both sides of the point.

Given that;

The function, f(x) = 6x + 1

And the function g(x) is a linear function which passes through the points (2 , 3) and (3, 7).

Since, The slope 'm' of any straight line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

And, m = d/dx (f(x))

So, The slope of function f (x) will be;

f(x) = 6x + 1

M = d/dx (f(x))

M = d/dx (6x + 1)

M = 6

And, Slope of linear function which passes through the points (2 , 3) and (3, 7) is;

m = (7 - 3) / (3 - 2)

m = 4/1

m = 4

Thus, The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

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\( \sqrt{147} \\ = \sqrt{3 \times 7 \times 7} \\ = 7 \sqrt{3} \)

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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The ratio of the number of minutes Declan rode his bike to the number of minutes he had soccer practice is x / (2.5x + 10)

An equation is an expression that shows the relationship between two or more variables and numbers.

From the table:

Number of minutes on ride bike = 2.5(x + 3) + 2.5 = 2.5x + 10

Ratio of ride bike to soccer practice = x / (2.5x + 10)

The ratio of the number of minutes Declan rode his bike to the number of minutes he had soccer practice is x / (2.5x + 10)

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Answer:

Yes

Step-by-step explanation:

     c+5

×        7

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

7c+35

=  7c+35-7

=7c+28

Answer:

\(a>6\)

Step-by-step explanation:

1) Subtract 1 from both sides.

\(a>7-1\)

2) Simplify 7 - 1 to 6.

\(a>6\)

Therefor, the answer is a > 6.

Answer:

a > 6.

Step-by-step explanation:

Move all terms not containing a to the right side of the inequality.

Inequality Form:

a > 6.

Answer:

7.49

Step-by-step explanation:

just add it up

Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer:

Circle= 4

triangle= 7

rectangular= 2

Step-by-step explanation:

if circle + circle is 8 so one circle is 4

and circle + rectangle is 6 so rectangle is 2

and if rectangle is 2 and rectangle+ triangle is 7because rectangle + triangle is 9 so if rectangle is 2 then 7 is left so 7 + 2 is 9

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Step-by-step explanation:

\(46064yx \times ( \frac{ { > < |x { \frac{( {))(6460 = 464}^{?} }{?} }^{?} | }^{?} }{?} \)

The expression that is equivalent to the following complex fraction (1-1/x)/2 is A) x-1/2x.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression given is:

(1 - 1/x) / 2

Simplifying the numerator will give (1 - 1/x) × 1/2

Taking x as LCD in numerator

(x - 1/x) × 1/2

(1 - 1/x) / 2 = x - 1 / 2x

The correct option is A.

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Which expression is equivalent to the following complex fraction?

(1-1/x)/2

A) x-1/2x

B) -1/2

C) 2x-2/x

D) 2x/x-1

Answer:

x=27/10

Step-by-step explanation:

move all the terms not containing x to the right side of the equation

Answer:

\(g(x) = \frac{1}{4}3^x +3\)

Step-by-step explanation:

Given

\(f(x) =\frac{1}{4}3^x -6\)

\(g(x) \to\) translate f(x) 9 units up

Required

Find g(x)

The translation rule is:

\(g(x) \to f(x) + 9\)

So, we have:

\(g(x) = f(x) + 10\)

\(g(x) = \frac{1}{4}3^x - 6 + 9\)

\(g(x) = \frac{1}{4}3^x +3\)

The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068