One pound of candies costs $3.50.
a) How much will we have to pay for 3 lb?
b)How much will we have to pay for 4.5 lb?
c)How many pound of candies can be bought for $7?
d)How many pound of candies can be bought for $10.50?

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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Answer:

It landed at a height of 14 feet

Step-by-step explanation:

Given

\(y = -\frac{1}{8}x^2 +4x\) --- Path of a t-shirt

\(3y = 2x - 14\) --- height of bleachers

Required

Height when t-shirts land in bleachers

\(3y = 2x - 14\)

Make y the subject

\(y = \frac{2}{3}x - \frac{14}{3}\)

Substitute \(y = \frac{2}{3}x - \frac{14}{3}\) in  \(y = -\frac{1}{8}x^2 +4x\)

\(\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x\)

Multiply through by 24

\(16x- 112 = -3x^2 +96x\)

Express as:

\(3x^2 + 16x -96x- 112 = 0\)

\(3x^2 -80x- 112 = 0\)

Using a calculator:

\(x = 28\) or \(x = -\frac{4}{3}\)

x can not be negative:

So:

\(x = 28\)

Substitute \(x = 28\) in \(y = -\frac{1}{8}x^2 +4x\) to calculate the height it landed

\(y = -\frac{1}{8} * 28^2 + 4 * 28\)

\(y = 14\)

The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.

Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).

The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.

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Answer:

( -2.5 , 1 )

Step-by-step explanation:

(-2.5 ,1 ) hope this helps u

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

x= 2

Step-by-step explanation:

3x – 5 = 1

Add 5 to each side

3x – 5+5 = 1+5

3x = 6

Divide by 3

3x/3 = 6/3

x= 2

Answer:

\(3x - 5 = 1 \\ 3x = 1 + 5 \\ 3x = 6 \\ x = \frac{6}{3} \\ x = 2 \\ thank \: you\)

Answer:

A. too much

Step-by-step explanation:

If we are only looking for how much water she drinks, we do not need to know the amount of hay or the amount of fruit

Answer:

To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:

(x, y) → (x + 2y - 5, y - 6)

Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:

A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)

Therefore, the coordinates of A' after the translation are (-3, -10).

Answer:

48 units

Step-by-step explanation:

36 is 75% of what number

36 = .75n

n = 36/.75

n = 48

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

The function was  \(\frac{5E (-9) }{2E(4) }\) :

We know that, E implies 10 to rise to power.

So, The equation above is Converted from scientific notation into standard form.

 \(\frac{5 x 10^-9 }{2 x 10^ 4 }\)

= 5/2  x 10 ⁻⁹⁻⁴

=2.5 x 10⁻¹³

Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

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Answer:

7 cups of coffee

Step-by-step explanation:

Given

\(n = 20 - 2.75c\)

Required

Find and describe the zero of the function

To do this, we simply equate n to 0

i.e.

\(n = 0\)

Substitute 0 for n in \(n = 20 - 2.75c\)

\(0 = 20 - 2.75c\)

Add 2.75c to both sides

\(0 + 2.75c = 20 - 2.75c + 2.75c\)

\(0 + 2.75c = 20\)

\(2.75c = 20\)

Divide both sides by 2.75

\(\frac{2.75c}{2.75} = \frac{20}{2.75}\)

\(c = \frac{20}{2.75}\)

\(c = 7.273\)

\(c = 7\) --- Approximated

This implies that the maximum cups of coffees that can be bought is 7

The question is missing some parts. Here is the complete question.

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost in type II ovens. A samplle of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with standar deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let \(\mu_{1}\) be the true mean repair cost for type I ovens and \(\mu_{2}\) be the true mean repair cost for type II ovens.

Step 1 of 4: State null and alternative hypothesis for the test.

Step 2 of 4: Compute the value of test statistics. Round your answer to 2 decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to 3 decimal places.

Step 4 of 4: Make the decision for the hypothesis test. (Reject or fail to reject Null Hypothesis)

Answer and Step-by-step explanation:

First, state null and alternative hypothesis:

\(H_{0}: \mu_{1}=\mu_{2}\)

\(H_{a}: \mu_{1}>\mu_{2}\)

Use z-statistics:

\(z = \frac{x_{1}-x_{2}}{y}\)

where x₁ and x₂ are the means and:

\(y=\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }\)

Calculating value of test stattistic:

\(y=\sqrt{\frac{(23.47)^{2}}{61}+\frac{75.25^{2}}{45} }\)

\(y = \sqrt{9.030+5.046}\)

\(y = \sqrt{14.076}\)

y = 3.752

\(z = \frac{79.6-75.25}{3.752}\)

z = 1.16

The test statistics is z = 1.16

The decision rule for rejecting null hypothesis is: \(\alpha\) ≤ test statistics

Using z-score table, it is possible to determine p-value, which is:

p-value = 0.877

Comparing p-value with level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.

Answer:

(a)  No, the binomial distribution does not applies to the scenario because each trial does not have the same probability of success.

(b) No, the binomial distribution does not applies to the scenario because x does not count the number of successes.

Step-by-step explanation:

Binomial distribution illustrates the probability of success or failure of any result of an experiment under study which is usually repeated several trials. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.

Binomial experiments are random experiment with fixed number of repeated trials. For example, let consider a random experiment in which a fair coin and a fair die are tossed together. We may wish to find the probability of a head and a 5 showing up in a single throw.

The event of a head and a 5 may be considered as a combination of two events:

The event E₁ of a head showing up in the throw of the coin does not in any way affect the event E₂ of a 5 showing up in the throw of die.

We say that the event E₁ and E₂ are independent, as such the outcome in one trial has no effect on the outcome in other trials.

In binomial distribution; we are concerned with two main variables;

From the information given in the question: The objective of the question from both a and b is to determine if the binomial distribution applies to the scenario in both  a and b ?

SO;

In (a) , given that:

You think that you will win the first bid with a probability of​ 25%;

The second through fourth bids with probability​ 30%.

Does the binomial distribution applies to this  scenario?

No, the binomial distribution does not applies to the scenario because each trial does not have the same probability of success.

In (b); given that:

Each bid is for​ $70,  and you think there is a​ 25% chance of winning a​ bid,

with bids being independent events. Does the binomial distribution applies to this  scenario?

No, the binomial distribution does not applies to the scenario because x does not count the number of successes.

Answer:

25

Step-by-step explanation:

When answer questions about unique combinations, there are usually two ways people go about finding the solutions.

First, sometimes it can take a while, but it often helps people visualize the question if they jot down or sketch each different combination. Then, they can just count them up at the end to find there answer.

The easeier way is to use a quick math trick. If you have 5 runners, with 5 potential lanes each runner could start in, you can just multiply these two variables together to get your answer of the number of possible options.

So,

5 runners * 5 lanes = 25 possible combinations for each lane and runner

The number of unique ways that the runner can be arranged in 5 lanes for a race is 120.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

Total number of runners = 5

Total number of lanes = 5

Number of ways that 5 runners can be arranged = 5! = 120

Hence the number of ways is 120.

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Answer:

74

Step-by-step explanation:

13x5+9=74

Answer:

area: 9

perimeter: 12

Step-by-step explanation:

Answer:

i gotchu

u=4a (equation for perimiter)

u=12

perimeter is 12

a=a2 (equation for area)

a=9

area is 9

:)

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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Answer:

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:

\(P=3S+5H\)

The restriction for cloth can be written as:

\(S+2H\leq500\)

The restriction for metal can be written as:

\(2S+3H\leq600\)

The restriction for wood can be written as:

\(4S+7H\leq800\)

The condition for S and H to be positive is:

\(S, H \geq0\)

Step-by-step explanation:

We have an objective function that, in this case, we want ot maximize.

This function is the Profit (P).

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:

\(P=3S+5H\)

We have 3 restrictions, plus the condition that both S and H are positive.

The restriction for cloth can be written as:

\(S+2H\leq500\)

The restriction for metal can be written as:

\(2S+3H\leq600\)

The restriction for wood can be written as:

\(4S+7H\leq800\)

The condition for S and H to be positive is:

\(S, H \geq0\)

Answer:

y=12x-16

Step-by-step explanation:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

Answer:

Yes

Step-by-step explanation:

Starting with 2, the step to the next number is 6.  Each step increases by 3.

When you are on 8, the next step is an increase of 9.  The next step is an increase of 12,  The next step not shown would increase by 15 for give you 44.

So the first step would be 3 below the number 6 which would be subtracted from 2 to give you - 1 as your first starting point.

The common difference is 3(n) where n is an integer starting with 0 and incrementing by 1 with each new Y2 and Y1 is  -1.

The equation Y2 = 3(n+1) + Y1    where n=0

Answer:

Step-by-step explanation:

The graph of the linear equation cuts the x-axis at (5,0)

Answer:

  144

Step-by-step explanation:

For a bitstring of length n, there are Fibonacci(n+2) strings containing no two consecutive zeros. This can be seen by constructing the strings starting with n=1.

1-bit strings: 1, 0 -- 2 strings not containing consecutive 0s

2-bit strings: 11, 10, 01 -- 3 strings not containing consecutive 0s

Note that we have added 1 to all the 1-bit strings, and added 0 only to the string ending in 1.

3-bit strings: 111, 110, 101, 011, 010 -- 5 strings not containing consecutive 0s

Note that these 5 strings consist of all (3) of the 2-bit strings with 1 appended, and all (1) of the 2-bit strings ending in 1 with 0 appended. The number that now end in 0 is the number previously ending in 1.

__

If (x, y) represents the numbers of n-bit strings ending in (0, 1), then the number of (n+1)-bit strings ending in (0, 1) is (y, x+y). That is, the recursive relation is ...

  \((x_1,y_1)=(1,1)\\(x_n,y_n)=(y_{n-1},\,x_{n-1}+y_{n-1})\\b_n=x_n+y_n\quad\text{number of n-bit strings without consecutive 0s}\)

For n=1 to n=10, these pairs are ...

  (1, 1), (1, 2), (2, 3), (3, 5), (5, 8), (8, 13), (13, 21), (21, 34), (34, 55), (55, 89)

The sequence of b[n] values is ...

  2, 3, 5, 8, 13, 21, 34, 55, 89, 144

which are the n=3 to n=12 numbers from the Fibonacci sequence.

That is, there will be Fibonacci(12) = 144 10-bit strings with no consecutive 0s.

According to the given data we have the following:

Debra started washing at 8:33 AM

finished at 9:22 AM

One easy way to find out the amount of time it took to her washing her clothes would be the following:

Debra started washing at 8:33 AM, so from 8:33 am to 9 o clock 27 minutes passed.

So, if she finished at 9:22 AM, that means that we would have to add to the 27 minutes another 22 minutes, so 27+22=49 minutes.

Therefore, it took to her 49 minutes to wash her clothes.