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vampirchik
17 days ago
12

John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John's words per mi

nute on a minute on a typing test. Then X~N(58,11)
Mathematics
1 answer:
Zina [9.1K]17 days ago
8 0

Answer:

When x = 72, the z score is:

z = \frac{72-58}{11}= 1.273

The average is 58

This z-score indicates that x= 72 is 1.273 standard deviations above the mean.

Step-by-step explanation:

Let’s consider the following details for this question: John's typing speed on a test is assumed to follow a normal distribution. Let X denote the number of words he can type in a minute. Hence, X ~ N(58, 11). It’s important to round the result to three decimal points if needed.

Provide your response below for words per minute on a typing test conducted on Sunday. The z score when x = 72 is

In this scenario, we acknowledge that the variable under consideration is represented by a normal distribution:

X \sim N (\mu= 58, \sigma=11)

The formula for the z score is as follows:

z = \frac{X -\mu}{\sigma}

By substituting values, we derive:

z = \frac{72-58}{11}= 1.273

The mean is 58

This z-score indicates that x= 72 is 1.273 standard deviations higher than the mean.

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Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere
Svet_ta [9486]

Answer:

The parametrization of the specified curve is x = 10 cos(t) \ \,z = 10 sin(t)

Step-by-step explanation:

From the provided problem statement, we derive the function

x^2 + y^2 + z^2 = 125

When y = 5

x^2 + 5^2 +z^2 =125

x^2 + z^2 = 100

x^2 + z^2 = 10^2

Converting the above to a polar equation yields

x = 10 cos(t) \ \,z = 10 sin(t)

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9 days ago
Kennedy has a gross income of $95,000. What is her total tax due?
AnnZ [9071]

Answer:

This brings her total gross income to $140,000 ($3,000 + $500 + $41,500 + $90,000 + $5,000), with her farm gross income being $95,000 ($90,000 + $5,000). Since 67.9% (which is at least two-thirds) of her gross income derives from farming ($95,000 ÷ $140,000 = .679), she qualifies for the special estimated tax rules designed for qualified farmers.

Step-by-step explanation:

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1 month 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 [9101]

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

7 0
1 month ago
Jamal is comparing his transportation options for an upcoming trip. He’s considering a rental car and a taxi service. Based on h
zzz [9066]
The set of rental car rates making it more economical for Jamal than employing taxi services is outlined as A = {x | 0 ≤ x < 26} [where x represents dollars]. The step-by-step breakdown is as follows: Let the rental cost be $x per day. With Jamal's trip extending over 4 days, factoring in $24 for gas, and estimating taxi costs at around $128, an inequality emerges: 128 > 24 + 4x. Thus simplifying leads to 4x < 104 and consequently x < 26.
3 0
6 days ago
Which is the solution of the quadratic equation (4y – 3)2 = 72? y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction a
Inessa [8989]

Answer:

y = \frac{3 + 6\sqrt{2} }{4} y y = \frac{3 - 6\sqrt{2} }{4}

y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction

Explicación paso a paso:

La ecuación cuadrática que tenemos es (4y - 3)² = 72

Debemos encontrar el valor de y.

Ahora, 4y - 3 = ± 6√2

⇒ 4y = 3 ± 6√2

⇒ y = \frac{3 + 6\sqrt{2} }{4} y y = \frac{3 - 6\sqrt{2} }{4}

Por lo tanto, las soluciones son y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction (Respuesta)

6 0
1 month ago
Read 2 more answers
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