Q 2. Using a standard deck of cards (which has 26 red cards and 26 black cards, with 13 cards of
every suit), what is the probability of selecting a red card, and then after replacing the card, selecting a
heart card?

-2

The range of the function is a set of all the values of y on the graph

The lowest point of the graph on the y-axis is -2

Therefore, the lowest value of the range of the function shown on the graph is -2

[tex]{\Large \begin{array}{llll} w=t^4 e^{\frac{2-t}{5+5t}} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ 4t^3e^{\frac{2-t}{5+5t}}~~ + ~~\stackrel{\textit{\LARGE product rule}}{t^4 \stackrel{\textit{\large chain rule}}{e^{\frac{2-t}{5+5t}}\cdot \stackrel{quotient~rule}{\cfrac{(-1)(5+5t)~~ - ~~(2-t)(5)}{(5+5t)^2}}}} \\\\\\ 4t^3e^{\frac{2-t}{5+5t}}~~ + ~~t^4 e^{\frac{2-t}{5+5t}}\cdot \cfrac{(-5-5t)~~ - ~~(10-5t)}{(5+5t)^2}[/tex]

[tex]4t^3e^{\frac{2-t}{5+5t}}~~ + ~~t^4 e^{\frac{2-t}{5+5t}}\cdot \cfrac{-15}{(5+5t)^2} \implies t^3 e^{\frac{2-t}{5+5t}}\left[4- \cfrac{15t}{(5+5t)^2} \right] \\\\\\ t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{(100t^2+200t+100)-15t}{(5+5t)^2} \right]\implies t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{100t^2+185t+100}{(5+5t)^2} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{dw}{dt}=t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{100t^2+185t+100}{(5+5t)^2} \right] \end{array}}~\hfill[/tex]

Answer:

They have an 89% satisfaction rate, less than the goal.

Step-by-step explanation:

To find this, divide 1068/1200, this gives you 0.89

This shows that they have an 89% satisfaction rate.

Since, the satisfaction rate 89% which is less than 90%. Therefore, management will take corrective actions.

Given that, if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

A survey of 1,200 customers showed that 1,068 were satisfied with their customer service.

Here, the satisfaction rate = 1068/1200 ×100

= 0.89 ×100

= 89%

Since, the satisfaction rate 89% which is less than 90%. Therefore, management will take corrective actions.

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Answer:

  (c)  32

Step-by-step explanation:

Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).

You want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).

Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.

  f(g(13)) = 32

ANSWER:

C. point of concurrency

STEP-BY-STEP EXPLANATION:

The only point where these lines cross each other is called the point of concurrency.

Therefore:

The point of concurrency is a point at which three or more lines intersect.

The correct answer then is C. point of concurrency

Answer:

x = 30

Step-by-step explanation:

2x + 15 = 3x - 15

--------------------------

2x + 15 = 3x - 15

-3x          -3x

----------------------

-x + 15 = -15

    -15     -15

-------------------

-x = -30

÷-1   ÷-1

----------------

x = 30

I hope this helps!

Answer:

r = 5%

Step-by-step explanation:

Formula : I=PRT

GIVEN:

I = 125

P = 5000

R = R

T = 6

125= (5000)(R)(0.5)

125=2500R

0.05=R

Interest rate = 0.05(100)

                    = 5%

7-(x^2+14x+49)

7-x^2-14x-49

-x^2-14x-42

Answer:

[tex]{ \tt{ { \sin}^{2} x + \cos {}^{2}x = 1 }}[/tex]

- Divide through by cos²x ;

[tex]{ \tt{ \frac{ { \sin }^{2}x }{ \cos {}^{2} x} + \frac{ \cos {}^{2} x }{ { \cos }^{2} x} = \frac{1}{ { \cos }^{2}x } }} \\ \\ { \boxed{ \tt{ { \tan}^{2} x + 1 = { \sec }^{2} x}}}[/tex]

- Divide tgrough by sin²x;

[tex]{ \tt{ \frac{ { \sin }^{2}x }{ { \sin}^{2}x } + \frac{ \cos { }^{2}x }{ { \sin}^{2}x } = \frac{1}{ { \sin}^{2} x} }} \\ \\ { \boxed{ \tt{1 + { \cot }^{2}x = \csc {}^{2} x}}}[/tex]

Answer:

See below for proof.

Step-by-step explanation:

Given trigonometric identity:

[tex]\large\boxed{\sin^2x+\cos^2x =1}[/tex]

To prove the identity 1 + cot²x = cosec²x :

[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\sin^2x$}\implies \dfrac{\sin^2x}{\sin^2x}+\dfrac{\cos^2x}{\sin^2x}& =\dfrac{1}{\sin^2x}\\1+\left(\dfrac{\cos x}{\sin x}\right)^2&=\left(\dfrac{1}{\sin x}\right)^2\\1+(\cot x)^2&=(\text{cosec}\: x)^2\\1+\cot^2x&=\text{cosec}\: ^2x\end{aligned}}[/tex]

To prove the identity tan²x + 1 = sec²x :

[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\cos^2x$}\implies \dfrac{\sin^2x}{\cos^2x}+\dfrac{\cos^2x}{\cos^2x}& =\dfrac{1}{\cos^2x}\\\left(\dfrac{\sin x}{\cos x}\right)^2+1&=\left(\dfrac{1}{\cos x}\right)^2\\(\tan x)^2+1&=(\sec x)^2\\\tan^2x+1&=\sec ^2x\end{aligned}}[/tex]

Additional identities used:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\\$\sec \theta=\dfrac{1}{\cos \theta}$\\\end{minipage}}[/tex]

Answer:

8

Step-by-step explanation:

8+8=16 see i helped u GIVE ME BRAINLIST NOW PLSS I BEG :.)

We have,

The given expression is,

This can be written as,

Answer:

$3.33 (rounded) per hour

Step-by-step explanation:

The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.

hours run per month = daily hours × days in month

hours run per month = 5 × 30

hours run per month = 150

if the total bill was $500 for 150 hours then:

$500 ÷ 150 = $3.33 (rounded) per hour.

Answer:

$2,875

Step-by-step explanation:

Interest = Principal x rate x time

Interest = $2500 x 0.03 x 5

Interest = $375

Original value + interest = Total amount

$2,500 + $375 = $2,875

Statement Problem: Two angles are supplementary . One angle is 5 less than four times the other . Find the measures of the angles

olution:

13 diamonds, y = 3 chandeliers, x = 52 diamonds, x = 130 diamonds, y = 40 chandeliers. this is the complete table using equivalent ratios.

When we compare any two kinds of ratios, they are said to be equivalent. To determine whether these two or more ratios are equivalent, they can also be compared to one another. For instance, the ratios 1:2 and 2:4 can be called as equivalent.

Simply put, a ratio is a comparison of two numbers. When a ratio is equal, the proportionate relationship remains constant. By multiplying the first value by the same ratio, or unit of proportion, you can determine your own equivalent ratios.

It is possible to treat an equivalent ratio and a proportion interchangeably. An equivalent ratio is the result of simplifying the two ratios to the same fraction.

Let us take the value of x -----> the number of diamonds

Let us take the value of y ----> the number of chandeliers

we know that

The ratio present between the number of diamonds to that of the number of chandeliers is equal to

[tex]\frac{x}{y} = \frac{39}{3}[/tex]

1) for y = 1,

x = 13 diamonds

2) for x = 39

y = 3 chandeliers

3) for y = 4

x = 52 diamonds

4) y = 10

x = 130 diamonds

5) x = 520

y = 40 chandeliers

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Answer: 52 and 130

Step-by-step explanation:

Total annual expense= $8400

Saving= $622,834,634,198.44

Compound interest is addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on principal sum plus previously accumulated interest. Compound interest is standard in finance and the economics.

Compound interest is contrasted with the simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

a)Total annual expense= total miles *average cost per mile

                                   = 30,000* 0.28= $8400

b)Amount deposited in 9 years= 8400*9= $75,600

total amount after 9 years= FV= PM[tex][(1+r)^{n}-1]/r[/tex]

                                           =8400* [tex][(1+8.5)^{9}-1]/8.5[/tex]

                                           =$622,834,709,798.44

Savings=622,834,709,798.44 -75600= $622,834,634,198.44

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If a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel

A jet engine close up produces sound at 152 decibels

The the relative intensity of one jet engine = [tex]126^{152}[/tex]

The relative intensity of a pair of jet engines = 2× [tex]126^{152}[/tex]

The reading of a pair of nearby jet engine in decibel = 10log(The relative intensity of a pair of jet engines)

Substitute the values in equation

The reading of a pair of nearby jet engine in decibel = 10×log(2× [tex]126^{152}[/tex])

= 168.62 decibel

Hence, if a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel

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a = 252, x = 7; y = 5925.13

Equation is given by the formula:

where:

yo = the initial population; r = growth rate, x = time

In your case, yo = 252. And the grow rate is 57%, therefore the r = 0.57. Finally, the exponential equation has this form:

Then, if we want to know what is the population after 7 days, we can evaluate this function:

By applying the elimination method the value of x is - 2 and y is 7.

This is a problem from algebraic equations and we have to apply the elimination method. We can solve this problem by following a few steps.

So, the given equation according to the question is,

− 2x = 4 ................ ( equation 1 )

4x + 2y = 6 ............... ( equation 2 )

While applying the elimination method we have to multiply equation (1) with the positive coefficient of x in the second equation and vice versa.

Here the coefficient of x in the first equation is 2 and in the second equation is 4.

Now, we have to multiply equation ( 1 ) with 4 and equation ( 2 ) with 2.

Therefore,

− 2x = 4 ................ ( equation 1 ) × 4

4x + 2y = 6 ............... ( equation 2 ) × 2

Now, we can rewrite the equations as,

− 8x = 16 .................. ( equation 3 )

8x + 4y = 12 .................. ( equation 4 )

Now the coefficient of x in both equations are same but opposite sign. So, we have to add the equations.

Here we get , -8x + 8x + 4y = 16 + 12

Or, 4y = 28

Or, y = 7

Now, we have to put the value of y in any equation.

4x + 2.7 = 6  ( equation 2 )

Or, 4x = 6 - 14 = -8

Or, x = -2

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The correct question :

By applying the elimination method, solve the following pair of simultaneous equations:

− 2x = 4

4x + 2y = 6

The amount of time 26 students spend on their phones represent by a dot plot:

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Answer:

See attachment.

Step-by-step explanation:

A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale.  

If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.

Given data set:

{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}

Label the increments on the given line to include the range of data.

Label them -2 to 16 increasing in 1 unit.

Label the dot plot with a suitable title describing what the dot plot represents.

Place "Time students spent on their phones on one given day (nearest hour)" under the line.

Count the number of data points for each discrete category:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Category & \sf Frequency\\\cline{1-2} 0 & 1\\\cline{1-2} 3 & 1\\\cline{1-2} 4 & 2\\\cline{1-2} 5 & 2\\\cline{1-2} 6 & 3\\\cline{1-2} 7 & 4 \\\cline{1-2} 8 & 4 \\\cline{1-2} 9 & 3\\\cline{1-2} 10 & 3\\\cline{1-2} 11 & 2\\\cline{1-2}12 & 1\\\cline{1-2}\end{array}[/tex]

Draw a stack of dots that number high for each category.

(See attachment).

The coordinates along the directed line segment is (-1/8, 1/4)

The points are given as:

A  = (3, 4)

B = (-2, -2)

The ratio on the segment can be represented as;

m : n = 5 : 3

So, we have the coordinates of the point Q that lies along the directed line segment to be

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

So, we have:

Q = 1/(5 + 3) * (5 * -2 + 3 * 3, 5 * -2 + 3 * 4)

Evaluate

Q = (-1/8, 1/4)

Hence, the coordinates of the point Q is (-1/8, 1/4)

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The correct answer is [a] m<BCD - m<DBC =10°

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves.

Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by the sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and the rotation's image, and it is centered at the rotation's center.

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Answer:

9, 4/4, and 1.00000

Explanation:

Whole numbers are the basic counting numbers 0,1,2,3,4,...There is no fractional or decimal part. And no negatives.

Given the numbers:

• Firstly, 9 is clearly a whole number

• 4/4 = 1. 4/4 is a fraction that is equivalent to a whole number. Therefore, it is a whole number.

• 1.00000=1. Whenever there is a decimal in which all the digits after the decimal point are zeros, the number is a whole number.

The property of a(b+(-b))=(b+(-b))a is called as Commutative Property of Multiplication.

The Commutative Property in mathematics is a rule that allows interchange the order of terms or factors without any change in the end result.

In multiplication, we can interchange the factors without affecting the end result of multiplication. For example, 2 x 3 = 3 x 2 = 6

In addition, we can interchange the terms without affecting the summation result. For example, 2+3 = 3+2 = 5

But Commutative Property does not apply to subtraction or division.

For example, 2-3 != 3-2

or, 2/3 != 3/2

Hence the answer to the question is Commutative Property of Multiplication.

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The provided line segment's midpoint is (x, y) =. (2, 0)

The midpoint of a line segment is referred to as the midpoint in mathematics. The third side of a triangle is parallel to the segment when two line segments of a triangle are joined. It is the average value of the coordinates' endpoints.

The provided coordinates for the line segment, according to the query, are: (7, 6) and (-3, -6).

The line segment's midpoint can be determined using the following formula:

Midpoints = [tex]\frac{x1+x2}{2} ; \frac{y1+y2}{2}[/tex]

And the values for calculating the midpoint are as follows: x1 = 7, x2 = 3, y1 = 6, y2 = -6.

When we enter these values into the formula, we obtain

Midpoint (x, y): (7 + (-3), 6 + (-6)

Mid point (x, y) equals 2 and 0

Hence, the halfway point for the given line segment is: (x, y) = (2, 0).

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Answer

Explanation

To determine the probability that the number rolled is odd using a standard die, we first list the total outcomes as shown below:

1,2,3,4,5,6

As we can see, the odd numbers are:

1,3,5

This means that the total favorable outcomes is 3.

Now, we use the formula:

We plug in what we know:

Therefore, the probability that the number rolled is odd is 1/2.

Answer:

3/6

A standard die has 6 sides, numbered 1 through 6 (1,2,3,4,5,6). That means we have 3 odd numbers (1,3,5)  and 3 even numbers (2,4,6).

The total possible outcomes of an odd number are 3, because there are 3 odd numbers, and the total outcomes are 6. So we write it as 3/6, like 3 out of six chances of getting an odd number.

It can be simplified to 1/2.

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The most appropriate choice for decimal will be given by-

The number is 68.830

What is decimal?

The type of numbers which has a whole number part and a fractional part and the whole number part is seperated from the fractional part by a decimal point is known as decimal.

Decimal can be terminating as well as non terminating

Terminating decimal numbers are those numbers which has finite number of figures after the decimal point.

Non terminating decimal numbers are those numbers which has infinite number of figures after decimal points.

Here,

The required number is the same as sixty-eight and 830 thousandths.

So, the number is 68.830

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The equations will be a+ y ≤ 13, since Micaela can't work more than 13 hours and also she needs to earn at least $140 each week, so other equation will be 13a + 10y ≥ 140.

Inequality, a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

a = number of hours spent tutoring

y = number of hours spent landscaping

Micaela can't work more than 13 hours, so a + y ≤ 13.

Also, she needs to earn at least $140 each week, so 13a + 10y ≥ 140.

Using intercepts, you may graph things in this format on paper. They must be transformed into slope-intercept form in order to be graphed on a standard graphing calculator.

For instance, if a = 12 and y = 2, then a + y = 13 hours, and 12(13) + 2(10) = $176. Micaela puts in her maximum number of hours and earns more than she should.

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Let:

Where:

k = scale factor

so:

now, we can find y and x: