Tamira is making trail mix. She has $80 to spend on a mixture of almonds and cashews. Almonds cost $8 per pound and Cashews cost $10 per pound. Let "x" represent the pounds of almonds and "y" represent the pounds of cashews. Write an equation to model this scenario.

Answer:

3

Step-by-step explanation:

The inequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,

x > 320.

And x > 320  means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

(a) Given, that the telephone company offers two billing plans for local calls. Plan 1 charges ​$35 per month for unlimited calls.

Plan 2 charges ​$19 per month plus ​$0.05 per call.

Let x calls be made,

Now, according to the Plan 1,

the charges for 'x' calls be ​$35 only

according to the Plan 2,

the charges for 'x' calls be

​$19 + $0.05x

Now, Plan 1 is more economical than Plan 2 for,

$35 < ​$19 + $0.05x

On solving the inequality, we get

$16 < $0.05x

On dividing both the sides by 0.05, we get

16/0.05 < x

320 < x

i.e. the monthly calls be more than 320.

(b) Now, as in part (a) we got,

320 < x

which means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

Hence, theinequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,

x > 320.

And x > 320  means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

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0.9660  is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

  If the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 29 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.  

Let X = (Number of defective ibuprofen tablets in a random sample of 29 tablets.)  Then we may reasonably assume that X follows a binomial distribution.  For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective).  Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome.  A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample.  The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.)   For this situation, we have p = .01 (since we are told 1% of the tablets in the shipment are defective) and n = 29.  The general formula for the binomial distribution is

P(x) = nCx·px·(1 - p)n-x

where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 29 tablets.)  The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order. It is given by

nCx = n!/[x!·(n-x)!]

where ! is the factorial symbol.

We want to find the probability that the shipment is accepted.  We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications.  That is, the number of defectives must be less than or equal to one.

P(Shipment accepted) = P(X ≤ 1).  (In this case, X ≤ 1 if and only if X=0 or X=1)= P(0) + P(1).

So we calculate P(0) (the probability of 0 defective tablets in the shipment), and P(1) (the probability of 1 defective.)  Using the formula for the binomial distribution, we have

P(0) = 29C0·(.01)0·(1 - .01)29 - 0.

But 29C0 = 1, so

P(0) = 1·(.01)0·(.99)29 ≅ .74717

Also,

P(1) = 29C1·(.01)1·(1 - .01)29 - 1.

Calculating 29C1, we have

    29C1 =  29!/[1!·(29-1)!] = 29, so

          P(1) = 29·(.01)1·(99)28

          P(1) ≅ .21887

Finally, then, we have

P(Shipment accepted) ≅ .74717 + .21887 ≅ .9660 (to 4 decimal places.)

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Answer:

1

Step-by-step explanation:

Change is y over the change in x

The y's are 4 and 7.

The x's are -1 and 2

[tex]\frac{4-7}{-1-2}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

The factor of the expression is [tex]49x^8-16y^{14} =(7x^4-4y^7)(7x^4+4y^7)[/tex].

What is factor?

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

Given, 49x⁸ − 16y¹⁴ is an expression.

We can write it as  (7x⁴)² − (4y⁷)²

we know, [tex]a^2-b^2=(a-b)(a+b)[/tex]

using this identity, we get

49x⁸ − 16y¹⁴ =  (7x⁴ - 4y⁷)(7x⁴ + 4y⁷)

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Target buys masks wholesale for $15 a piece. They mark them up 150% for resale. If Kara bought one from them and paid 12% sales tax, then

The amount spent by Kara overall is $42.

Here, we need to determine how much money she spent overall. Finding the mask’s cost after adding the 150% mark is the first step in determining how much is spent.

She purchased it for $37.5 but had to pay 12% tax on it. Consequently, she spent $42 total.

Use proportional relationships to solve multi step ratio and percent problems. Examples include simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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The equation to describe the information that 2 less than 4 times x is 4x - 2.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, 2 less than 4 times will be:

= (4 × x) - 2

= 4x - 2

Therefore, the equation is 4x - 2.

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Step-by-step explanation:

What is the value?

Please put the full question

Then only I would be able to help you

Answer:

50

Step-by-step explanation:

Since 45-45-90 tri, x^2+x^2=100^2

So 2x^2=10000

2x=100 and x=50

Answer:

a = 70.71068 = 50√2

Step-by-step explanation:

a = √c^2 - b^2

= √1002 - 70.7106781186552

= √5000

= 70.71068 = 50√2

Thanks.

Answer:

Step-by-step explanation:

Answer:

k=5

Step-by-step explanation:

15-8k+15k-8=42

15+7k=50

7k=35

k=5

According to the ratio, it doesn't make sense to have a total of 9 people in the dance competition.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

The ratio of boys to every girls is 3:2 in a dance competition.

Let's find if it will make sense to have a total of 9 people in the competition.

Therefore,

number of boys = 3 / 5 × 9 = 27 / 5 = 5.4

number of girls = 2 / 5 × 9 = 18 / 5 = 3.6

Therefore, it doesn't make sense to have 9 people in the competition because the actual number of boys and girls will be in decimal which is impossible.

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The graph of f(x) = (3/4)ˣ is attached. The values are f(-2) = 16/9, f(-1) = 4/3, f(0) = 1, f(1) = 3/4 and f(2) = 9/16

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the exponential function:

f(x) = (3/4)ˣ

Hence:

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

The graph of f(x) = (3/4)ˣ is attached.

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X=3

sbzhshsbsnjsjsjsnsnsnns

Answer:

50000 ppppp567765

Step-by-step explanation:

Everytime you can come over and play with your hair

In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle

Here the given postulate is sas  postulate

The sas stands for Side - Angle - Side postulates

The congruent is defined as the two shapes that has same size and shape.

Two triangles can be proved congruent by using the sas, sss, asa postulates

According to sas postulate of the triangle, if two sides and one angle of the triangles must be equal to the two sides and one angle of second triangle

Hence, In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle

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The probability is 0.2322.

From the question, we have

Probability that the person who visit her restaurant will spend at least $125 is : p = 0.4

Total number of people : n= 8

Probability that 4 will spend at least $125,

P(X=4)= 8C4(0.40)^4 (1-0.4)^4

=0.2322

Probability:

Probability is another word for possibility. This area of mathematics examines how random events happen. The value might be between 0 and 1. Mathematicians have used probability to forecast the likelihood of certain events. In general, probability relates to how likely something is to happen. You can better understand the potential results of a random experiment by using this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to ascertain how likely something is to occur. Many things are difficult to foresee with absolute confidence.

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The probability that 10 squared centimeters of dust contains more than 10140 particles is 0.1841

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

The mean asbestos particles in 1 cm2 is given as 1000, therefore in 10 cm2 of dust, the mean number of particles is given as: 1000*10 = 10,000

The number of particles here is given as:

X ~ Poisson(y = 10000)

Therefore the normal approximation here is given as:

X Nu = 10000,02 = 10000)

The probability here is computed as:

P(X > 10090)

Converting it to a standard normal variable, we get here:

10090 – 10000 P(Z > V10000

P(Z > 0.9)

Getting it from the standard normal tables, we get here:

P(Z > 0.9) = 0.1841

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Answer:

x = 2 , y = 29

Step-by-step explanation:

if the quadrilateral is to be a parallelogram , then

• opposite sides are congruent

• opposite angles are congruent

Then

2x + 9 = x + 11 ( subtract x from both sides )

x + 9 = 11 ( subtract 9 from both sides )

x = 2

and

3y + 19 = 106 ( subtract 19 from both sides )

3y = 87 ( divide both sides by 3 )

y = 29

The amount Gabriela paid with the discount is $50.4.

Discount is a reduction in price. Discount means reducing the price or value of an object or item.

Gabriela bought a new pair of glasses at the store when they were 30% off the sale.

The regular price of the glasses is 72 dollars. The amount Gabriela paid with the discount can be calculated as follows:

discount = 30% off of the sale

discount = 30 / 100 × 72

discount = 2160/ 100

discount = 21.6 dollars

Therefore,

price paid with the discount = 72 - 21.6

price paid with the discount = 50.4 dollar

Therefore, the amount she paid with the discount is 50.4 dollars

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Answer:

Step-by-step explanation:

Move all terms not containing xx from the center section of the inequality.

Inequality Form:

0<x<30<x<3

Interval Notation:

(0,3)

Answer:

y=-4

x=-3

Step-by-step explanation:

x=3y/4

5*(3y/4) +6y+39=0

15y/4+6y+39=0

3.75y+6y+39=0

9.75y=-39

y=-4

x=-3

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 12 +4}{2}~~~ ,~~~ \cfrac{ -4 +9}{2} \right) \implies \left(\cfrac{ 16 }{2}~~~ ,~~~ \cfrac{ 5 }{2} \right)\implies \left( 8~~,~~2\frac{1}{2} \right)[/tex]

Answer:

£600

Step-by-step explanation:

Katie gives 1/3 of the money to her sister.

1/3 of 1200 is 400, because 1200 divided by 3 is 400. So she gives 400 to her sister, which means she has 1200-400= 800 left.
When she gives 1/4 of the remaining to her brother, that means that we need to figure out how much 1/4 of 800 is. 800 divided by 4 is 200. So Katie gives 200 to her brother.

800 that she has remaining minus the 200 she gives to her brother leaves her with 800-200 = 600

His new grade will be 85.838 , this can be calculated using simple fraction.

What is fraction?

As the components of a whole, fractions are by definition. The entire can be a single item or a collection of items.

Main Body:

Initial percentage of child = 93.73%

Child's percentage at test = 74%

according to the question his 40% of test grade is accounted

Parts of grade is from test = 4/10

So his new grade = (4/10)*74 + (6/10) *93.73

New grade = 29.6 +56.238

Hence the new grade for the child will be 85.838%

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Step-by-step explanation:

5.

normally no.

just think - we are talking about people. it's it possible to have half of a friend at a game ?

no, the input is not possible.

but if this function is used in the context or a larger analysis, and mean values are created and checked, then it might be valid.

it all depends on the context of how the function is used.

2.

we don't see all answer options, but the range is the interval or set of all valid y-values (the 2nd number in an ordered pair).

we see : -1, 3, 4, 6

whichever answer option shows this is correct.

Question 1

y = mx+7

5 = m*(-2)+7

5 = -2m+7

-2m+7 = 5

-2m = 5-7

-2m = -2

m = -2/(-2)

===============================================

Question 2

y = 2x+c

4 = 2(1)+c

4 = 2+c

4-2 = c

2 = c

The inverse function is f⁻¹(x) = √(x + 5) - 2. And the value of 'x' when the inverse function is 2 will be 11.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

f(x) = (x + 2)² - 5,       x > 2

The inverse function of the function will be given as,

x = [f⁻¹(x) + 2]² - 5

[f⁻¹(x) + 2]² = x + 5

f⁻¹(x) + 2 = √(x + 5)

f⁻¹(x) = √(x + 5) - 2

If the value of the inverse function is 2, then the value of x is given as,

2 = √(x + 5) - 2

4 = √(x + 5)

16 = x + 5

x = 16 - 5

x = 11

The inverse function is f⁻¹(x) = √(x + 5) - 2. And the value of 'x' when the inverse function is 2 will be 11.

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The inequality of the graph shown below is  y ≤ -x - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality provides a comparison between non equal numbers and variables.

The inequality shown is a straight line passing through (-4, 0) and (0, -4). The equation of the straight line is:

y - 0 = [(-4 - 0)/(0- (-4)](x - (-4))

y = -1(x + 4)

y = -x - 4

The inequality is a thick line to the left. Hence it is  y ≤ -x - 4

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Answer:  an = 18 - 3n

Step-by-step explanation:

so the next term should be 3