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8 days ago

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Harper knows he is 50 yards from school. The map on his phone shows that the school is 34 inch from his current location. How fa

r is Harper from home, if the map shows the distance as 3 inches? Enter your answer in the box.

2 answers:

PIT_PIT [3.8K]8 days ago

8 0

To solve this question, follow the steps outlined below:

1. Since 1 yard equals 36 inches, to convert 50 yards to inches involves:

$(50)(36)=1800in$

2. If he is standing 50 yards away from the school, and the map indicates that the school is 34 inches away from him, when it shows 3 inches the actual distance is:

$\frac{(1800in)(3in)}{34in}=158.82in$

3. If you express this back in yards:

$\frac{158.82}{36} =4.41 yd$

Consequently, the answer is: 158.82 inches or 4.41 yards.

Zina [3.8K]8 days ago

4 0

The real distance from Harper to the school is 50 yards.

As per the map, the distance from the school is represented as 34 inches.

This indicates that 34 inches equates to 50 yards.

Hence, 1 inch equals 50/34 = 25/17 yards.

To calculate the actual distance of 3 inches in yards, we multiply the yard value of 1 inch by 3.

Thus, 3 inches results in 3* 25/17 = 75/17 = 4 7/17 yards, which is approximately 4.412 yards in decimal form.

Consequently, the distance from Harper's home is 4 7/17 yards or approximately 4.412 yards if the map indicates 3 inches.

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Suppose your statistics professor reports test grades as z-scores, and you got a score of 1.57 on an exam. a) Write a sentence

tester [3895]

Answer:

a) In this case, we have a z-score of 1.57, characterized as:

$z =\frac{x -\mu}{\sigma}$

This signifies that our score is 1.57 standard deviations above the average of all test scores.

b) $P(Z$

Using the normal standard distribution or Excel, we computed:

$P(Z$

This represents 2.275% of the dataset.

Step-by-step explanation:

Previous concepts

Normal distribution denotes a "probability distribution that is symmetric around the mean, indicating that data close to the mean occurs more frequently than data further from it".

The Z-score serves as "a statistical measurement representing a value's relation to the average (mean) of a set, calculated in terms of standard deviations away from the mean".

Solution to the problem

Part a

For this instance, we hold a z-score of 1.57, which is defined as:

$z =\frac{x -\mu}{\sigma}$

This shows that our score is 1.57 deviations above the overall test score average.

Part b

A z-score of z=-2 indicates that your friend's score is 2 deviations below the other test scores.

Assuming a normal distribution, we can derive the percentage:

$P(Z$

Using the normal standard distribution or Excel, we discovered:

$P(Z$

This represents 2.275% of the data.

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12 days ago

If mJI = (3x+2)°, mHLK = (15x-36)°, and m∠HML = (8x-1)°, find mHLK

lawyer [3979]

Response:

The measure of mHLK is "(204)°".

Step-by-step breakdown:

Given values include:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

What is mHLK?

Now,

Utilizing the chord-chord angle formula, we find

$mHMK=\frac{1}{2}(mJL+mHLK)$

Inserting the known values into the equation gives us

⇒ $(8x-1)=\frac{1}{2}(15x-36+3x+2)$

By carrying out cross-multiplication, we arrive at

⇒ $2(8x-1)=18x-34$

⇒ $16x-2=18x-34$

By subtracting "18x" from both sides, we obtain

⇒ $16x-2-18x=18x-34-18x$

⇒ $-2x-2=-34$

Upon adding "2" to both sides, we end up with

⇒ $-2x=-34+2$

⇒ $-2x=-32$

⇒ $x=\frac{32}{2}$

⇒ $x=16$

By substituting the value of "x" into mHLK = (15x-36)°, we calculate

⇒ (15x-36)° = (15×16-36)°

⇒ = (240-36)°

⇒ = (204)°

Thus, mHLK = (204)°

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1 day ago

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

PIT_PIT [3895]

Answer:

The tangent plane equation for the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

We have

The ellipsoid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation for the tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ (Given)

The hyperboloid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The tangent plane equation at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The tangent plane equation for the hyperboloid is

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The tangent plane equation

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required tangent plane equation for the hyperboloid is

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

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12 days ago

The hourly wage increases each employee receives each year depends on the number of years of service. Every three years of servi

Inessa [3895]

Answer:

________{0.50 if x < 3

________{1.00 if 3 ≤ x < 6

f(x) = ____{1.50 if 6 ≤ x < 9

________{2.00 if 9 ≤ x < 12

Step-by-step explanation:

Based on the details provided:

Employees with less than 3 years receive an increase of $0.50 hourly

Employees with at least 3 years but under 6 years receive $1.00 increase hourly

Employees with a minimum of 6 years and less than 9 get $1.50 increase hourly

Employees with at least 9 years but below 12 years receive $2.00 increase hourly

This information can be expressed as a piecewise function:

________{0.50 if x < 3

________{1.00 if 3 ≤ x < 6

f(x) = ____{1.50 if 6 ≤ x < 9

________{2.00 if 9 ≤ x < 12

The conditions are outlined in the piecewise function above with x indicating the number of years employed.

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5 days ago

Lines m and n are cut by transversal l. Lines m and n are cut by transversal l. On line m where it intersects line l, 4 angles a

babunello [3607]

∠1 and ∠8 are alternate exterior angles while ∠3 and ∠6 are alternate interior angles.

step-by-step explanation:

When transversal l intersects lines m and n, the angles formed outside each line on the opposite side of the transversal constitute alternate angles (like ∠1 and ∠8). In contrast, alternate interior angles appear on opposite sides but are located between the two lines (like ∠3 and ∠6).

Learn More

Keywords: Transversal, angles

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12 days ago

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