A merchant has coffee worth $50 a pound that she wishes to mix with 20 pounds of coffee worth $80 a pound to get a mixture that can be sold for $60 a
pound. How many pounds of the $50 coffee should be used?

$10.12 will Cassie pay in all for the pair of binoculars after sales tax is included.

What is sales tax?

A sales tax is a fee that is paid to the government when specified products and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are often used to describe taxes on goods and services that consumers pay directly to a governing authority.

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87

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The bearing of C from A is 60° South.

How does one calculate bearing from A to B?

When AN elongates the angle will be 180°

Then the angle between A and C:

35° + 85° + x = 180°

120° + x = 180°

x = 180° - 120°

x = 60°

Hence, The bearing of C from A is 60° South.

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The length of the building on the scale drawing is found as 16 centimeters.

For the given data in the question-

Dimensions of the building;

Dimensions of the drawing of the building;

Thus, taking ratios of Height to length

125/80 = 25/x

On simplification;

x = 80 x 25 / 125

x = 16

Thus, the length of building on the scale drawing is found as 16 centimeters.

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The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.

As per the given data,

we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

We know that,

Probability(Event) =Number of Favorable Outcomes/Total number of

                                Outcomes = x/n.    

Total number of Outcomes is 52 (given)

So,  we will calculate Number of Favorable Outcomes as follows:

The total no. of King in deck of card is 4

The total no. of queen in deck of card is 4.

The total no. of ace in  deck of card is 4.

The total no. of jack in deck of card is 4.

Therefore, the number of favorable outcomes is 4+4+4+4= 16

Now, putting values in the above stated formula of probability, we get:

Probability= 16/52=4/13

Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.

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The equation of a line that passes through point (5,7) and parallel to the graph of y = 2/3x - 7 is y = (2/3)x + 11/3

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Where m is slope.

Given the equation of the graph  y = (2/3)x - 7

Using the slope intercept form where m is slope.

y = mx + b

y = (2/3)x - 7

Slope of the graph will be;

Slope m = 2/3

Next, find the line parallel to the graph and which passes through the point (5,7).

Using the point slope formula

y - y₁ = m( x - x₁ )

Plug in the slope and point.

y - 7 = (2/3)( x - 5 )

Solve for y

y - 7 = (2/3)x - 10/3

y = (2/3)x - 10/3 + 7

y = (2/3)x + 11/3

Therefore, the equation of line parallel to the graph is y = (2/3)x + 11/3.

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Answer:

25 + y

Step-by-step explanation:

It looks like you might be missing some information.

Answer:

0.25 − 3

=0.25 + −3

= −2.75

( a number line to help to)

Step-by-step explanation:

The measure of the exterior angle is 60°.

What is the Exterior Angle Theorem?

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

We have,

interior angles:

∠ABC = z + 10

∠BAC = 4z

Exterior angle:

∠ACB = z + 50

Exterior Angle Theorem:

The measure of exterior angle = Sum of two opposite interior angles’ measure.

According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠BAC would be equal to the exterior angle ∠ACB.

∴ ∠ABC + ∠BAC =  ∠ACB

  z + 10 + 4z = z + 50

5z = z + 40

z = 40/4

∴  z = 10

so, the value of the z is 10.

exterior angle:

∠ACB = 10 + 50 =60

Hence, the measure of the exterior angle is 60°.

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Answer:

117$.

Step-by-step explanation:

Let $x$ represent the number of cards in Wei Jing's collection. We are given that $70 \leq x \leq 150$. We are also given that $x \equiv 3 \pmod{10}$ and $x \equiv 5 \pmod{9}$. Since $x \equiv 3 \pmod{10}$, $x - 3$ is divisible by 10. Since $x \equiv 5 \pmod{9}$, $x - 5$ is divisible by 9. The least common multiple of 10 and 9 is $90$, so $(x - 3) - 90$ is divisible by 90 and $(x - 5) - 90$ is divisible by 90. Adding these equations gives us $2x - 98$ is divisible by 90. Dividing both sides by 2 gives us $x - 49$ is divisible by 45. Since $70 \leq x \leq 150$, the only solution for $x$ is $x = 117$.

The area enclosed by the curves f(x) and g(x) is  1/12

Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.

When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.

Let our given curves be :

f(x) = x² and g(x) = x³ within the interval [0,1]

Formula to calculate area under these curves is

=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]

Interval is given from 0 to 1

Therefore ,

=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]

Integrating,

=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]

=> 1/3 - 1/4

=> 1/12 is required area

The given question is incomplete So, I've answered the question in general

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The price of a ticket to the homecoming dance to maximize the council's profit is 4830.

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Answer:

$2 each ticket

Step-by-step explanation:

I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.

The Jocelyn estimate's percent error is 2.181 centimeters..

What is percent error ?

Percent error calculates the difference between an estimate and a right number and expresses it as a percentage. Analysts can use this statistic to determine how big the mistake is in relation to the actual number. It is also referred to as % error and percentage error.

There are three steps to determining the % error:

1. Determine the error, which is the estimated value minus the actual value.

2. Multiply by the accurate value.

3. In order to create a percentage, multiply by 100.

Given information:

The size of a piece of wood (Exact value)= 5.5 cm

if it really does measure(Approximate value)=5.62 cm

percentage error={(approximate value-exact value)/exact value}×100

percentage error = ((5.62-5.5)/5.5)×100

percentage error = 2.181cm

Consequently, 2.181cm is the Jocelyn estimate's percent error.

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A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows

Margin of error  = 0.05 = E

z-score = z/2 = 1.645

n = 0.27 x 0.73 (1.645/ 0.05)²

n = 213.343

n=214

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The margin or error associated with the confidence interval is 5.62 points

The sample size of the third grade children = 20

The confidence interval for the population mean score  = 90%

The mean score = 64 points

The standard deviation = 12 points

The degree of freedom = The sample size - 1

= 20 - 1

= 19

The critical value of t at degree of freedom 19 = ±2.093

The margin error = Critical value of t × [tex]\frac{s}{\sqrt{n} }[/tex]

Substitute the values in the equations

The margin error = 2.093 × [tex]\frac{12}{\sqrt{20} }[/tex]

= 2.093 × 2.68

= 5.62 points

Therefore, the margin error is 5.62 points

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The graph of the equation y = (1/3)x + 2 is passing through points  

(3, 3) and ( -3, 1).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A linear equation y = (1/3)x + 2.

Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.

When x = 3, y = 3 ⇒ (3, 3).

When x = - 3, y = 1 ⇒( -3, 1).

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Answer:

Your answer is 416 + 13 [tex]\sqrt{5}[/tex].

Step-by-step explanation:

The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.

Given are the similar triangles,

1) Δ HJG ~ Δ CAB

Scale factor = 3:1

2) Δ NPM ~ Δ ABC

Scale factor = 1:2

3) KJML ~ CDAB

Scale factor = 1:2

4) 40/x = 20/5

x = 10

5) 18/x = 21/7

x = 6

6) 6/3 = x/15

x = 30

Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

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The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

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The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

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a) The given function is [tex]$\frac{x^2-2x+2}{(x-1)^2(x+2)}$[/tex]. The series of this function is [tex]$\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$[/tex]. Therefore, the series is alternating (-1).

b) The sum of the first four nonzero terms of the series is [tex]$-1x^1+2x^2-3x^3+4x^4$.[/tex]

c) The interval of convergence is [tex](-2, 1)[/tex]. This is because the denominator [tex]$(x-1)^2(x+2)$[/tex] has a zero at [tex]$x=-2$[/tex] and a zero at [tex]$x=1$[/tex], and the function is undefined at these two points. Therefore, the interval of convergence is the open interval  [tex]$(-2, 1)$[/tex].

Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.

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a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:

E = {11, 15, 24, 33, 42, 51}

b) The probability of E is 6/36 = 1/6.

c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:

F = {11, 15, 22, 31, 33, 42, 44, 51}

d) The probability of F is 2/9.

Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.

The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.

So, the probability of E is 6/36 = 1/6.

The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.

So, the probability of F is 8/36 = 2/9.

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Answer: x = 9/10 - 7/10

Step-by-step explanation:

The given triangles are congruent to each other by the rule of (AAS) Angle Angle side.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given figure in the question,

There are two given triangles in the question,

Δ ABC and Δ MNO

As we can see that,

∠ C = ∠ M

∠ B = ∠ N and,

The side, AC = OM

So, Δ ABC ≅ Δ MNO

So, by using AAS (Angle Angle Side) rule, triangle ABC and triangle MNO are congruent to each other.

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Answer: Susie is correct.

Step-by-step explanation:

Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.

a²+b² = c²

a = 9

b = 12

c = 17

9² + 12² = 17²

==> 81 + 144 = 289

==> 225 = 289, This is not true

Therefore this triangle is not a right triangle.

a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.

b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.

c) E(x) = 1/p

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...

Geometric Distribution :

The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.

The Geometric Random Variable can be written as X ~ G(p).

The probability mass function is P(X = x) = (1  - p)ˣ⁻¹ p

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Answer:

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

Given:

Find the missing sides:

Perimeter is:

The adding property of equality should be used to satisfy the given equation.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

-15 + x/3 = 18

Add 15 on both sides of the equation

So, we have

45 + x = 18 × 3

x = 54 + 45

x = 99

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The change in temperature based on the information is 27°F.

It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.

Let the change in temperature be represented by x.

Therefore, -10 + x = -17

x = 17 + 10

x = 27

The Temperature is 27°F.

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After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?