You jump 3 1/2 feet. How far do
you jump in inches?

Hello!

[tex]-5x - 7 > 3x + 1\\\\-5x - 3x > 1+7\\\\-8x > 8\\\\\boxed{x < -1}[/tex]

Size of the house should be 2900 ft².

Correct option is B.

We have,

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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complete question:

A house is listed for sale at $235,000, but the listing does not include square

footage of the house. Based on the comps, the line of best fit is

y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house

be?

OA. 2850 ft2

OB. 2900 ft2

OC. 20,000 ft²

OD. 2350 ft²

The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.

Given that,

Mass of the sculpture of the earth = 829 kg

We know that,

Mass of an hydrogen atom = 2 × 10⁻²⁷ kg

Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom

                                              = 829 / 2 × 10⁻²⁷

                                              = 414.5 × 10²⁷

                                              = 4.145 × 10²⁹

Hence the required number of atoms is 4.145 × 10²⁹.

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Answer:

a)

Step-by-step explanation:

the function is 11x6=66+13=79x¹=79

hope it helps

37 and 1/2 % of 104 is 39 .

Given,

37 and 1/2 % of 104

Simplifying further,

Convert mixed fraction into simple fraction,

37 and 1/2 %  = 75/2%

Now,

75/2% of 104

= 75/2 ×1/100×104

=39 .

Hence 39 is the required answer.

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By the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

Since, The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean μ and standard deviation σ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ / √n.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The mean for the entire population is 5.7 years.

So, by the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

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The number of terminates are 2,384.78.

An exponential function can be used to illustrate the daily growth of termites.

If "t" represents the number of days, then "N" represents the number of termites.

⇒ N = [tex]1600(1 + 0.042)^{t}[/tex]

Where 0.042 is the decimal form of 4.2%.

Using this formula,

It can be  calculate the number of termites after any number of days t.

For example,

After 10 days, the number of termites would be:

⇒ N = [tex]1600(1 + 0.042)^{10}[/tex]

⇒ N = [tex]1600(1.042)^{10}[/tex]

⇒ N ≈ 2,384.78 termites

Hence,

⇒ N =  2,384.78 termites

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The graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

To graph the given equations, we'll plot the points that satisfy each equation and then connect them to form a line.

Equation 1: y = -1

This equation represents a horizontal line passing through the y-coordinate -1. Regardless of the x-coordinate, the y-value remains constant at -1. Therefore, we plot a point at (0, -1) and draw a horizontal line through that point.

Equation 2: 3x - y = 4

To graph this equation, we can rewrite it in terms of y:

y = 3x - 4

Now we can choose a few x-values, substitute them into the equation, and solve for y to obtain the corresponding y-values. Let's select three x-values: -2, 0, and 2.

For x = -2:

y = 3(-2) - 4

y = -6 - 4

y = -10

For x = 0:

y = 3(0) - 4

y = -4

For x = 2:

y = 3(2) - 4

y = 6 - 4

y = 2

Now we have three points: (-2, -10), (0, -4), and (2, 2). Plotting these points on the graph, we can draw a line connecting them.

In summary, the graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

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The value of 13.3km/L corresponds to 30.595 miles/gal

The conversion required is 13.3km/L to mile/gal

converting km to miles

1km = 0.621371 miles

13.3 km = ?

cross multiplying results to

? = 13 * 0.621371 = 8.077 miles

converting L to gallons

1 liters = 0.264172

hence we have that

= 8.077 / 0.264

= 30.595

thus, 13.3km/L is equal to 30.595 miles/gal

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Using the formula for two events not mutually exclusive, the probability of ordering either one is given as 0.8.

Since we assume that the events are not mutually exclusive, this implies that the occurrence of event B is not affected by the probability of occurrence of event A.

Then, the probability of ordering either one is the sum of their individual probabilities minus the probability of ordering both.

The probability formula is:

p (chocolate or vanilla) = p (chocolate) + p (vanilla) - p (chocolate and vanilla)

p (chocolate) = 0.6

p (vanilla) = 0.5

p (chocolate or vanilla) = 0.6 + 0.5 - 0.6 * 0.5

= 1.1 - 0.3

= 0.8

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Step-by-step explanation:

I believe it is asking for the probability that x is greater than the mean + two standard deviations .....

  look at the mean ....count up two SD ( labelled at the bottom)  ....then see what is to the right of this point  : 2.35 % + .15 % =  2.5%  is greater

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

The triangles ABC and CDE are similar

The width AB of the river is 172.73 ft

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and CDE

The above triangles have corresponding angles and they also have similar side lengths

This means that the triangles are similar

Here, we have the following ratio

AB : 100 = 38 : 22

So, we have

AB/100 = 38/22

This gives

AB = 100 * 38/22

Evaluate

AB = 172.73

Hence, the width AB of the river is 172.73 ft

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Answer:

Step-by-step explanation:24 ft

The interest rate that satisfies the assumption is approximately 5.33%.

We have,

To find the interest rate that satisfies the assumption, we can use the formula for compound interest:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case, we have:

P = $400

A = $684

t = 11 years

Let's substitute these values into the formula and solve for r:

$684 = $400 x [tex](1 + r)^{11}[/tex]

Dividing both sides by $400, we get:

[tex]1.71 = (1 + r)^{11}[/tex]

Now, we need to isolate (1 + r) by taking the 11th root of both sides:

[tex](1 + r) = 1.71^{1/11}[/tex]

Using a calculator, we find:

(1 + r) ≈ 1.0533

Subtracting 1 from both sides, we get:

r ≈ 0.0533

To express the interest rate as a percentage, we multiply by 100:

r ≈ 5.33%

Therefore,

The interest rate that satisfies the assumption is approximately 5.33%.

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The missing root is -24 - 5i.

To find the missing root of the polynomial function f(x) = x^3 - x^2 + 24x + 26, we can use the fact that the sum of all the roots of a polynomial equation is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term.

In this case, the coefficient of the second-to-last term is 24, and the coefficient of the leading term is 1. Therefore, the sum of all the roots is -24/1 = -24.

We already know that -1 and 1 + 5i are roots, so we can subtract them from the sum to find the missing root:

Missing root = -24 - (-1) - (1 + 5i) = -24 + 1 - 1 - 5i = -24 - 5i.

Note that the missing root is a complex number, indicating that the polynomial has at least one complex root.

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By the Centroid Theorem, the lengths are given as follows:

4. GZ = 12 units.

5. OT = 14.4 units.

The Centroid Theorem states that the centroid of a triangle is located two-thirds of the total distance from each vertex to the midpoint of the opposite side.

Hence for length GZ we have that:

GZ = 2GU/3

GZ = 2 x 18/3

GZ = 12 units.

For length OT, we have that:

ZT = 1/3OT

OT = 3ZT

OT = 3 x 4.8

OT = 14.4 units.

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The measure of each missing indicated side of the triangle would be given as follows;

1.) X = 2.7

2.) X = 15.2

For question 1.)

Using the sine formula such as given below;

a/sinA = b/sin B

where ;

a = X

A = 27°

b = 6

B = 90°

That is;

X/sin27° = 6/sin90°

X = 6×0.453990499/1

= 2.7

For question 2.)

a/sinA = b/sin B

where ;

a = X

A = 47.4°

b = 14

B = 180-(47.4+90)

= 180-137.4

= 42.6

That is;

X/sin47.4° = 14/sin42.6°

X = 14×0.736097087/0.676875969

= 10.305359218/0.676875969

= 15.2

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x = ±π/6 + πn, ±11π/12 + πn, where n is an integers are solutions of the equation  cos²x = sin²x + 1/2

To solve the equation cos²x = sin²x + 1/2, we can use the trigonometric identity sin²x + cos²x = 1.

Rearranging the equation, we have:

cos²x - sin²x = 1/2

Using the identity cos²x - sin²x = cos(2x), we can rewrite the equation as:

cos(2x) = 1/2

The solutions to this equation can be found by taking the inverse cosine (or arccosine) of both sides:

2x = ±π/3 + 2πn, ±11π/6 + 2πn, where n is an integer

Dividing both sides by 2, we get:

x = ±π/6 + πn, ±11π/12 + πn, where n is an integers

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The calculated coordinates of point B on line AB is (-1, 0)

From the question, we have the following parameters that can be used in our computation:

P =  (1,2)  

A = (2,4)

Also, we have

m : n = 1 : 2

The coordinates of point P are calculated using

P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

(1, 2) = 1/(1 + 2) * (1 * x + 2 * 2, 1 * y + 2 * 4)

Evaluate

(3, 6) = (x + 4, y + 6)

So, we have

x = -1 and y = 0

Hence, the coordinates of point B on line AB is (-1, 0)

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Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]

Now we solve for V₂:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]

Where:

Now, we substitute the values in the formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]

The price per shirt when 100 shirts are sold is of $5.

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 graph of the function, two points are given as follows:

(0, 20) and (20, 100).

Hence the slope is given as follows:

m = (100 - 20)/(20 - 0)

m = 4.

Hence the cost function is of:

y = 4x + 20.

For 20 shirts, the cost is of $100, hence the cost per shirt is given as follows:

100/20 = $5 per shirt.

The problem is given by the image presented at the end of the answer.

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The area of the logo 1 in square feet is  38.465 ft²

Remember that the area of a circle of radius R is given by the formula:

A = 3.14*R²

Here we can see that the radius of the circle is (1/2 in), but we wat the are in square feet, so let's write that in feets.

1 in = 7ft, then:

(1/2 in) = (7/2 ft) = 3.5 ft.

Replace that in the formula for the area:

A = 3.14*(3.5 ft)²

A = 38.465 ft²

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Answer: [tex]\sf\$6.48[/tex]

Step-by-step explanation:

If a six-pack of cola is sold for $1.50, then the price per can is:

[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]

A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:

[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]

The sales tax is 8%, so the tax on the purchase is:

[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]

Therefore, the total charge including sales tax is:

[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]

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The volume of the moon can be shown to be 3.07% of the volume of the planet.

First, calculate the radius of the planet and the moon.

The radius (r) of the planet is half of its diameter:

r = 27, 998 mi / 2

= 13, 999 mi

The volume of the planet is V:

= 4 / 3 π ( 13, 999 mi)³

=  11, 493, 372, 846 cubic miles

The volume of the moon is:

V = 4 / 3 π (4,059.71 mi) ³

=  352, 432, 952 cubic miles

The Percent volume :

= ( Volume of moon / Volume of planet) x 100

= ( 352, 432 ,952 cubic miles / 11, 493,372,846 cubic miles) x 100

= 3.07 %

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The traveler will need (y / x) dollars to purchase y yen.

To determine the number of dollars the traveler will need to purchase a certain amount of yen, we need to divide the desired amount of yen by the exchange rate.

Let's assume the traveler wants to purchase y yen.

and, the exchange rate is 1 dollar = x yen.

To find the number of dollars, we can set up the following equation:

y yen × (1 dollar / x yen) = (y / x) dollars

Therefore, the traveler will need (y / x) dollars to purchase y yen.

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To calculate the number of dollars needed to purchase a specific amount of Japanese yen, we'll need the exchange rate between the two currencies. However, the exchange rate provided in your question is missing. Please provide the exchange rate between the US dollar (USD) and the Japanese yen (JPY) so that I can help you calculate accurately.

Step-by-step explanation:

Wherever the fxn = 0  is where it touches the x -axis

0=(x-5)^3 (x+2)^2   means that one or both of the factors is 0

     (x-5)^3    is zero at   x = 5

      (x+2)^2  is zero at    x = -2

sooo    5 and  -2  

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except for the value x = -11/3.

The range of the reciprocal function f(x) = -7/(3x + 11), we need to determine the set of all possible values that f(x) can take.

The reciprocal of a number is obtained by taking the multiplicative inverse, which means that the reciprocal of a non-zero number a is 1/a.

We are looking for the range of the reciprocal function, so we need to consider the range of the expression (3x + 11).

The range of (3x + 11) is the set of all real numbers, except when the denominator becomes zero.

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except when (3x + 11) equals zero.

To find the x-value when (3x + 11) equals zero, we solve the equation:

3x + 11 = 0

Subtracting 11 from both sides, we get:

3x = -11

Dividing by 3, we find:

x = -11/3

The reciprocal function is undefined at x = -11/3, as it would result in a division by zero.

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