Find the slope and y-intercept of this linear function:
2x + x = 4(y - 1)

The pattern can be written as a whole number by the general equation written as, \(E = \dfrac{n} { 10^k }\).

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Decimal equivalent to 12 with zero tenths and hundredths: 12.00

To divide 3 by powers of 10, we can simply move the decimal point to the left by the same number of places as the exponent of 10. For example:

3 ÷ 10 = 0.3

3 ÷ 100 = 0.03

3 ÷ 1000 = 0.003

and so on.

So in general, to divide a whole number n by a power of 10 with exponent k, we can write:

The pattern can be written as:-

\(E = \dfrac{n} { 10^k }\)

Then we can move the decimal point in the numerator k places to the left to get the decimal equivalent.

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Answer:

\(P(1\ and\ 2) = 0.3309\)

Step-by-step explanation:

Given

\(Red = 3\)

\(Blue = 4\)

\(Orange=10\)

Required

Probability of selecting 2 orange marbles

The total number of marbles is:

\(Total = Red + Blue + Orange\)

\(Total = 3 + 4 + 10\)

\(Total = 17\)

The probability that the first selection is orange is:

\(P(1) = \frac{10}{17}\)

Because it is a selection without replacement, the number of orange marbles and the total number of marbles would decrease by 1, respectively.

So, the probability that the selection is orange is:

\(P(2) = \frac{10-1}{17-1}\)

\(P(2) = \frac{9}{16}\)

The required probability is:

\(P(1\ and\ 2) = P(1) * P(2)\)

\(P(1\ and\ 2) = \frac{10}{17} * \frac{9}{16}\)

\(P(1\ and\ 2) = \frac{10*9}{17*16}\)

\(P(1\ and\ 2) = \frac{90}{272}\)

\(P(1\ and\ 2) = 0.3309\)

The probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles is 0.3309.

Given that,

Jacob has a bag of his favorite marbles.

It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange.

We have to find,

What is the probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles.

According to the question,

It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange.

Total number of marbles = 3 + 4 + 10 = 17

The probability that the first selection of orange is,

\(P(1) = \dfrac{10}{17}\)

The selection without replacement, the number of orange marbles and the total number of marbles would decrease by 1, respectively.

\(P(2) = \dfrac{10-1}{17-1}\\\\P(2) = \dfrac{9}{16}\)

Therefore,

The required probability is,

\(P(1 \ and\ 2) = P(1) \times P(2)\\\\P(1 \ and \ 2)= \dfrac{10}{17} \times \dfrac{9}{16}\\\\P(1 \ and \ 2) = \dfrac{90}{272}\\\\P(1 \ and \ 2) = 0.3309\)

The probability that the selection is orange is 0.3309.

Hence, The probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles is 0.3309.

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Answer:

True

Step-by-step explanation:

If you divide 180 by 30 you will get 6. then 6 times 5 is 30. If you add 30 to 330 you will get 360. If you take 180 boxes for 30minutes and double. You get 360 boxes in 60minutes. If 5 minutes is 30 boxes. Subtract 30 from 360 and you get 330 in 55 minutes.

Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

Answer:

1632 inches squared

Step-by-step explanation:

Hi!

So the formula for area is length times width.

So you would multiply the length by the width which is 34 times 48 to get the area which is 1632 in squared.

Hope this helps!

To complete the square, we want a number such that:

because in this way we can writte the square as follows:

Hence the answer is the last option:

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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Answer:

JK MEANS Jungkook from BTS!

9514 1404 393

Answer:

  3.8%

Step-by-step explanation:

The interest on a simple-interest loan is ...

  I = Prt

where P is the principal value, r is the annual rate, and t is the number of years.

Solving for r, we get ...

  r = I/(Pt) = 608/(4000×4) = 0.038 = 3.8%

The annual interest rate for the loan was 3.8%.

Answer:

The logarithmic function can be written exponentially as follows.\(t = 8^y.\)

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is \(log_{8}(t) = y.\)

We know that if we have an equation in the form \(a^x = b\), we can rewrite it in logarithmic form as \(log_a(b) = x\) and vice versa.

Thus, \(log_{8}(t) = y\)

\(t = 8^y\)

Hence, the logarithmic function can be written exponentially as follows.\(t = 8^y.\)

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The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄

There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.

Now, we are given the fraction as an improper fraction in the form of 2³₄.

Rewriting as a whole number and a fraction gives:

2 + ³/₄

Breaking down the whole number into a fraction is done as:

1 + 1 + ³/₄

= ⁴/₄ + ⁴/₄ + ³/₄

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Answer:

1.34 × 10^3 is the answer

Answer:

Ok

Step-by-step explanation:

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

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Answer:

-22

Step-by-step explanation:

-4 + (5 - 2)(-6)

-4 + (3)(-6)

-4 + (-18)

-4 - 18

-22

Best of Luck!

Step-by-step explanation:

4^2/3

but I got 4^-3/3

hope help ful

A graph that represent the system of quadratic equations is shown in the image attached below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

By expanding the bracket, we have:

f(x) = (x - 4)(x + 4)

f(x) = x² - 4x + 4x - 16

f(x) = x² - 16

Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).

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Note that the equation for the parent function y=x² stretched horizontally by a factor of 4 and shifted down 5 units is given as follows: y = (1/16)x² - 5

Note that a parent function is a simple, basic function from which other more complex functions can be derived by applying transformations.

To stretch the graph horizontally by a factor of 4, we divide x by 4, which gives:

y = (1/16)x²

To shift the graph down 5 units, we subtract 5 from the whole function, which gives:

y = (1/16)x² - 5

Therefore, the equation for the parent function y=x^2 stretched horizontally by a factor of 4 and shifted down 5 units is:

y = (1/16)x² - 5

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Answer:

640

Step-by-step explanation:

The features of the given polynomial graph are;

A) Domain: (-∞, ∞)

Range: (-∞, 16)

B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)

C) The y-intercept is; (0, 0)

D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)

E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) Even function

The domain of a function is defined as the set of all possible input values for which the function holds. The range of a function is defined as the set of all possible output values for all possible input values.

A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.

B) The x-intercepts are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)

C) The y-intercepts are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)

D) Looking at the given graph, it is increasing when the curve rises  and in this case it is; (-∞, -2) and (0, 2)

E)  Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) The function is an even function

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Answer:

A

 \(P(X =  8 ) =  0.0037\)

B

    \(P(X < 5) =  0.805\)

C

I will not be surprised because the probability that fewer than half covered their mouth when​ sneezing is less than 0.5

Step-by-step explanation:

From the question we are told that

   The probability a randomly selected individual will not cover his or her mouth when sneezing is \(p = 0.267\)

    The probability a randomly selected individual will cover his or her mouth when sneezing is

                   \(q = 1 -p\)

                   \(q = 1 -0.267\)

                    \(q = 0.733\)

Generally the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing is mathematically represented as

        \(P(X =  8 ) =  \left 12 } \atop {}} \right. C_8 *  p^8 *  q^{12-8}\)

        \(P(X =  8 ) = 495 *  (0.267)^8 *  (0.733)^{12-8}\)

        \(P(X =  8 ) =  0.0037\)

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when​ sneezing is mathematically represented as

       \(P(X <  5 ) =  P[ P(X = 0) + \cdots + P(X =  4)]\)

=>        \(P(X <  5) = \left 12 } \atop {}} \right. C_0 *  (0.267)^0 * (0.733)^{(12- 0) }+\cdots +  \left 12 } \atop {}} \right. C_4 *  (0.267)^0 * (0.733)^{(12- 4) }\)

=>     \(P(X < 5) =  0.805\)

Give that half of  12 is  6 then

The probability that fewer than half covered their mouth when​ sneezing is mathematically represented as

      \(P(X > 6) =  1 -  P( X \le 6 )\)

  => \(P(X > 6)  =  1 -  [P(X = 0 ) +\cdots+P(X = 6) ]\)

 => \(P(X > 6) = 1 -  [\left 12 } \atop {}} \right. C_0 *(0.267)^0 *  (0.733)^{12 - 0 } +\cdots + \left 12 } \atop {}} \right. C_6 * (0.267)^6 *  (0.733)^{12-6}]\)

=>    \(P(X > 6)   =  0.0206\)

Answer:

116.62m

Step-by-step explanation:

\(c= \sqrt{a^2+b^2} = \sqrt {100^2+60^2} approx. 116.61904\)

If n is an integer and m + 5 is odd, then n must be even.

To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.

Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.

Therefore, we have shown that if n is odd, then m + 5 is even.

By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.

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The sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

Sample space refers to the set of all possible outcomes of a random experiment or a probability event. In the context of your card example, the sample space is the set of all possible cards that could be chosen from the labeled set.

In this case, the sample space would be {E, X, P, R, S, I, O, N}, as these are the possible outcomes when selecting one card from the set.

Therefore the sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

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Answer:

Step-by-step explanation:

this is hard maybe ask your mom