A box is filled with 5yellow cards, 8blue cards, and 7green cards. A card is chosen at random from the box. What is the probability that the card is not blue?

Complete Question

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Answer:

The  calcium level that is the borderline between low calcium levels and those not considered low is  \(c = 8.68\)

Step-by-step explanation:

From the question we are told that

    The mean is  \(\mu = 9.5\ mg/dL\)

     The standard deviation \(\sigma = 0.5 \ mg/dL\)

    The proportion of the population with low calcium level is  \(p =\)5% = 0.05

Let X be a X random calcium level

  Now the  P(X < c) = 0.05

Here P denotes probability

        c is population with calcium level at the borderline

  Since the calcium level is normally distributed the z-value is  evaluated as

    \(P(Z < \frac{c - \mu}{\sigma } ) = 0.05\)

The critical value for 0.05 from the standard normal distribution table is

       \(t_{0.05} = -1.645\)

=>    \(\frac{c - \mu}{\sigma } = -1.645\)

substituting values

       \(\frac{c - 9.5}{0.5 } = -1.645\)

=>    \(c - 9.5 = -0.8225\)

=>     \(c = 8.68\)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

3% of 70 means "0.03 x 70" which is 2.1.

The sales tax is $2.10.

Answer:

second option

Answer:

I got the exact question so pls hit me up when you find the answer

Step-by-step explanation:

Answer: 625 steps per hour

Step-by-step explanation:

10,000/16=625

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

Answer:

Step-by-step explanation:

2) False.

3) True. It could be 50°-65°-65°.

4) True. It could be 35°-35°-110°.

5) True. It could be 40°-50°-90°.

Answer:

3 7/15

Step-by-step explanation:

Hi,

4 (1/5 +2/3)

Find common denominators...

1/5 = 3/15

2/3 = 10/15

Add...

13/15

Now, multiply...

4 (13/15)

52/15

Simplify...

3 7/15

Hope this helped :)

Answer:

18x+15

Step-by-step explanation:

This is basically asking you to simplify the expression.

5(4x+3)-2x

Distribute the 5

20x+15-2x

Combine like terms (x values)

18x+15

Answer:

A probability cannot be more than 100%

\( \large{\underline{\textsf{\textbf{\purple{ Given : }}}}} \)

• Length = 9 \( \sf \dfrac{1}{2} \) yd = \( \sf \dfrac{19}{2} \) yd

• Breadth = 6 yd

• Height = 4 \( \sf \dfrac{2}{3} \) yd = \( \sf \dfrac{14}{3} \) yd

\( \large{\underline{\textsf{\textbf{\purple{ To \: calculate : }}}}} \)

• Volume

\( \large{\underline{\textsf{\textbf{\purple{ Calculation : }}}}} \)

As we know that,

\(\bigstar \: \boxed{\sf {Volume_{(Cuboid)} = \ell \times b \times h}} \\ \)

So,

→ Volume = \( \sf \dfrac{19}{2} \) yd × 6 yd × \( \sf \dfrac{14}{3} \) yd

→ Volume = ( \( \sf \dfrac{19}{2} \) × 2 × 14 ) \( \sf yd^3 \)

→ Volume = 19 × 14 \( \sf yd^3 \)

So, option (i) is correct.

Answer:

x = 7, y = 45

Step-by-step explanation:

\(7x+13=6x+20\)

\(x=20-13\\x=7\)

Angle

\(7(7)+13=49+13=62^{0}\)

supplementary angle

180 - 62 = 118°

\(3y-17=118\)

\(y=\frac{118+17}{3} =135/3=45\)

Hope this helps

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

Answer:

You can buy 12 pizzas and 20 sodas with a small sum left over.

Step-by-step explanation:

The purchase value of an office computer is $12,500. Its annual depreciation is $1875. then the value of the computer after 6 years is

1250

What is the simple definition of depreciation?

The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used.

The value of the computer is decreasing by $1875 annually per year. So the amount of decrease in 6 years is: 6×1875=$11250 6 × 1875 = $ 11250

now

The purchase value of an office computer is $12,500

therefore

12500- 11250

= 1250

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According to the the video, the Golden Ratio is a figure in mathematics theorized by mathematicians as a value that indicates natures beauty symmetry

\(\mathbf{The \ value\ of \ the \ Golden \ ratio \ is \ \phi} = \mathbf{\dfrac{1 + \sqrt{5} }{2} }\)

Good examples of the Golden Ratio in art and architecture is the Great Pyramid of Giza, constructed in 2570 B.C. and the temple of Parthenon for which construction began in 447 BC and the decoration completed in 432 BC

The reason the temple of Parthenon is so interesting is that the temple just like the pyramid were meant to last indefinitely, such that they can only be made to last so long by the deities, as such by building using the Golden Ratio found in nature including the spiral galaxies, is in recognition of nature's beauty which is aesthetically pleasing to the eyes, harmonious, and maybe preservative

2. The common presence of the Golden Ratio in the universe can be seen as both a grand design and a coincidence, however, due to the higher prevalence than random occurrence, it can be taken as a design that can be observed in nature

3. The topic helps reinforce the belief in the application of math to daily life, because it is a good portrayal of how math can contribute to all aspect of human life

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Answer:

Step-by-step explanation:

for additional examples of the Golden Ratio. Select your favorite example from the video (or your own research) and explain

why this specific example is so interesting to you. (Possible keywords: the golden ratio + in nature, + in art, + in the human body, + in geometry).

If initial sample of 458 grams of a radioactive substance decays according to the function \(A(t)=458e^{-0.038t}\) then the half-life of the substance is 0.

Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.

Given,

An initial sample of 458 grams of a radioactive substance decays according to the function

\(A(t)=458e^{-0.038t}\)

We need to find the half life

\(458=458e^{-0.038t}\)

Divide both sides by 458

\(1=e^{-0.038t}\)

Take log on both sides

\(log1=-0.038t\)

0=-0.038t

t=0

Hence, the half-life of the substance is 0.

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The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

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Calculate :

\( \frac{1}{10} \times \frac{17}{18} = \frac{1 \times 17}{10 \times 18} = \frac{17}{180} \)

Answer:

17/180

Step-by-step explanation:

You multiply both of the tops together and both of the bottoms together.

1 x 17 = 17

over

10 x 18 = 180

Hope this helps :D

Answer:

The equation of the line through the point (2, 5) that cuts off the least area from the first quadrant is \(y = -2.321\cdot x +9.642\).

Step-by-step explanation:

From Analytical Geometry we get that the equation of the line is represented by:

\(y = m\cdot x + b\) (Eq. 1)

Where:

\(x\) - Independent variable, dimensionless.

\(y\) - Dependent variable, dimensionless.

\(m\) - Slope, dimensionless.

\(b\) - y-Intercept, dimensionless.

From (Eq. 1) we find that intercepts are:

x-Intercept

\(x_{i} = -\frac{b}{m}\)

y-Intercept

\(y_{i} = b\)

And the area done by the line in the first quadrant is:

\(A = \frac{1}{2}\cdot x_{i}\cdot y_{i}\)

\(A = \frac{1}{2}\cdot \left(-\frac{b}{m} \right) \cdot b\)

\(A = -\frac{b^{2}}{2\cdot m}\) (Eq. 2)

If we know that \((x, y) = (2,5)\), then the equation of the line is reduced into this:

\(2\cdot m + b = 5\)

\(b = 5-2\cdot m\) (Eq. 3)

And we apply (Eq. 3) in (Eq. 2):

\(A = -\frac{(5-2\cdot m)^{2}}{2\cdot m}\)

\(A = -\frac{25-20\cdot m +4\cdot m^{2}}{2\cdot m}\)

\(A = -\frac{25}{2}\cdot m^{-2}-10+2\cdot m\) (Eq. 4)

The first and second derivatives are, respectively:

\(A' = 25\cdot m^{-3}+2\) (Eq. 5)

\(A'' = -75\cdot m^{-4}\) (Eq. 6)

Then the first derivative is equalized to zero and solved:

\(25\cdot m^{-3}+2=0\)

\(25\cdot m^{-3} = -2\)

\(25 = -2\cdot m^{3}\)

\(m^{3} = -\frac{25}{2}\)

\(m = -2.321\)

And the second derivative is evaluated at critical value:

\(A'' = -75\cdot (-2.321)^{-4}\)

\(A'' = -2.584\)

The critical value is associated with a positive area. Then, the y-intercept is: (\(m = -2.321\))

\(b = 5-2\cdot (-2.321)\)

\(b = 9.642\)

Therefore, the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant is \(y = -2.321\cdot x +9.642\).

The horizontal compression by a factor of 2 of a function f(x) is expressed as:

Now, for a downward shift of 6 units:

If the parent function is:

Now, combining the transformations above:

1. the equation is y=mx+b. m= slope and b= y-intercept so your answer should be y=2/3x+2

2. point-slope form is y-y1/x-x1=m answer is y+4=-1(x-1)

3. i give up im sorry my brain is fried ;-;

4.uhh i graphed it and attached an image lol

dang i- cant do no more math today lol sorry good luck

The radian solutions of the equation are θ = 2.71 and θ = 0.43 radians

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

-sin² (θ) - 2sin (θ) + 1 = 0

Divide through by -1

So, we have

sin² (θ) + 2sin(θ) - 1 = 0

Let y = sin(θ)

So, we have

y² + 2y - 1 = 0

When solved graphically, we have

y = 0.414 and -2.414

This means that

sin(θ) = 0.414 and sin(θ) = -2.414

Take the arcsin of both sides

θ = 2.71 and θ = 0.43

Hence, the angles are θ = 2.71 and θ = 0.43

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Answer:

500 tiles

Step-by-step explanation:

First find the area of the hall=10ft×(10ft×5)=500ft²

Number of tiles required=500ft²÷1ft²=500

Answer:

the second one

Step-by-step explanation:

it's negative 1 so it would be at negative 1