Write 28 as a product of its prime factors, write factors in order from smallest to largest

Answer:

The correct answer is 15 potatoes.

Step-by-step explanation:

To solve this problem, we can determine the unit rate and use proportions. We know that Sarai needs 6 potatoes for 16 latkes. We want to know how many potatoes she will need to make 40 latkes. Let's call this unknown value x. We can set up the following equation:

6 potatoes/16 latkes = x potatoes/40 latkes

To solve this equation, we can first simplify the left side to find the unit rate.

3 potatoes/8 latkes = x potatoes/40 latkes

To solve, we can recognize that 40 latkes is 5 times the amount shown in the unit rate (8 latkes), which means that we need 5 times the amount of potatoes.

3 potatoes * 5 = 15 potatoes

Therefore, the correct answer is 15 potatoes. Note that you could have also just solved the equation for x to find your answer as well.

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(a) Determinant: det(A) = -18; Rank: rank(A) = 4. The determinant and rank are non-zero, so the vectors are linearly independent.(b) Determinant: det(A) = 0; Rank: rank(A) = 3. The determinant is zero and the rank is less than 4, so the vectors are linearly dependent.

(a)

2 4 5 -3

-3 2 7 0

9 2 4 6

3 2 -6 5

Det = -18

(b)

1 -1 3 2

-1 2 4 -5

3 -4 2 9

7 2 1 3

Det = 0

The determinant and rank of the vectors can be used to determine whether or not they are linearly dependent. If the determinant is non-zero and the rank is equal to the number of vectors, then the vectors are linearly independent. If the determinant is zero and the rank is less than the number of vectors, then the vectors are linearly dependent.

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Answer:

Step-by-step explanation:

You could use 1 3/4's of a cup and 8 1/4's of a cup.

1 of the 3/4 cups is 3/4 so that covers the 3/4 of the cups of how much flour is needed.

8 of the 1/4 cups is 8/4 which is equal to 2 so that covers the rest of the flour needed.

And 2 + 3/4 is 2 3/4 which is the amount of flour that is needed.

OR

You could use 3 3/4's of a cup and 2 1/4's of a cup.

3/4 + 1/4=4/4

3/4+1/4=4/4

4/4 + 4/4 is the same thing as 1+1 which is 2, so that covers the 2 cups of the flour that is needed, and then you add another 3/4, now you have

2 3/4, which is the amount of flour needed.

(I think that there might be other ways/combinations but I only included 2..)

There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.

Let p1 be the proportion of local seniors and p2 national seniors.

H₀ : p₁ =  p₂

Hₐ : p₁ > p₂

(right tailed test at 5% significance level)

Group I II  

Success 69 60 129

Total 100 100 200

p 0.69 0.6 0.645

q 0.31 0.4 0.355

se 0.046249324 0.048989795 0.033836002

p diff 0.09  

Std error 0.03384  

Z 2.659574468 0  

p 0.00391  

we find that p value is 0.00391 < 0.05

Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

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Answer:

1. 600 yd^3

2. 103,680 in^3

Step-by-step explanation:

1. To find volume we do l*w*h

(15)(8)(5)

120(5)

600 yards^3

2. We also find the volume for this

(36)(60)(48)

2160(48)

103680 in^3

Hopes this helps

The solution for the given equation is am = -15.

The given equation is -2(am + 4) = 22

On simplifying the given equation for its solution, we get

-2(am + 4) = 22

⇒ -2am - 8 = 22

⇒ -2am = 22 + 8

⇒ -2am = 30

∴ am = -30/2 = -15

So, the solution for the given equation is -15.

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In the given circle with center O, DF is congruent to BC.

What is congruent?

When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.

Consider the given circle with center O.

We have to find DF is congruent to which line.

Let point E and A are the midpoints of chord DF and BC.

There is angle 90 degrees on both the points.

The chords DF and chord BC are on the same distance from the center of the circle which is 3.09.

So, the chords DF and BC are of same measure.

Therefore, the chord BC is congruent to DF.

Hence, in the given circle with center O, DF is congruent to BC.

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Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.

(a) The process is not a statistical process .

b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.

(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74

and Tolerance = 0.01 USL LSL = 0.01

After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995

cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686

(ii) Cp = min (Cpu, CP).

Cpu = 37.005-37 0.073 = 0.06849

CPL = 0.06859

Срк = 2 × 0.06849 = 0.024

The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).

This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).

The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.

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Answer: 50.24

Step-by-step explanation:

The formula to find the circumference of a circle is two pi r. So we just have substituted value into our formula. So we have To multiply by pi, so let's use 3.14 multiplied by our sequence to eight, so this is equal to 16, multiply by 3.14, which is equal to 50.24.

Answer:

Step-by-step explanation:

∛8.1 = 2.00829885025 it has accuracy up to 6 places which means the error is less than at least 8 decimal places .

For example ,

Using the first three terms of the Taylor series expansion of

f(x)=∛x  centered at

x = 8, approximate inmate ∛8.1 :

f(x) = ∛x≈2  + (x-8) / 12 - (x-8)² / 288

the first three terms shown will be sufficient to provide a good approximation for ∛x . Evaluating this sum at x = 8.1 gives an approximation for ∛8.1

f(8.1) = ∛8.1 ≈2 + (8.1 -8)/ 12 - (8.1 - 8 )² / 288

       = 2.00829861111

   ∛8.1 = 2.00829885025  

With just three terms, the formula above was able to find the approximate accuracy in ∛8.1 to six decimal places .

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Answer:$85.5

Step-by-step explanation:

So divide 66.50 by 7 and that will get you 9.5 then multiply that by 9 which is then 85.5

Answer:

Step-by-step explanation:

3250 : 156 = y : 40

y = 3250 × 40 : 156

y = 833.(3)                                    3 repeating

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

check

3250 : 156 = 833.(3) : 40

20,83333333333333 = 20,83333333333333

the answer is good

The height of Jane will be 38 9/30 inches.

The process of combining two or more numbers is called the Addition.

Given that;

Trina is 54 3/4 inches tall. Morgan is 1 1/2 inches taller than Trina and Jane is 1 1/5 inches taller than Morgan.

Now,

Since, Trina is 54 3/4 inches tall.

And, Morgan is 1 1/2 inches taller than Trina.

Hence, The height of Morgan = 54 3/4 + 1 1/2

                                              = 219/4 + 3/2

                                              = 219/4 + 6/4

                                              = 225/4

And, Jane is 1 1/5 inches taller than Morgan.

Hence, The height of Jane = 225/4 + 1 1/5

                                          = 225/4 + 6/5

                                          = (1125 + 24)/30

                                          = 1149/30

Thus, The height of Jane = 38 9/30 inches

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Answer:

-11

Step-by-step explanation:

To find f(3), we simply need to plug 3 in for x in the function f(x) = -3x-2. This gives us:

f(3) = -3(3) - 2 = -9 - 2 = -11

Therefore, the value of f(3) is -11.

We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

What is Normally distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15

            [tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]

            [tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]

The confidence interval ⇾ 0.0752 < µ < 0.1676

We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

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Answer:

Square Root of 80 in Radical Form: 4√5.

Step-by-step explanation:

√80 = 4√5. Meaning that the square root of 80 in radical form 4 √ 5.

OR Decimal form: 8.944

(Not sure if you wanted it in radical form... I also included it in decimal form)

To determine the maximum or minimum value of a given function, Lagrange multipliers are used.

What is langrange multipliers?

Let's set up everything now. We want to optimize (i.e., find the minimum and maximum value of) a function, f, under the condition that g (x, y, and z) = k. (x, y, and z). Once more, the equation that describes the boundary of a region may or may not be the constraint. Although the process is actually quite simple, there are times when the workload seems quite overwhelming.

Solve the following system of equations.

∇f(x,y,z) = λ

∇g(x,y,z)

g(x,y,z)= k

If there are minimum and maximum values, enter them into f(x,y,z) along with all of the solutions (x,y,z) from the first step.

∇ g ≠ → 0 at the point.

The constant, λ, is called the Lagrange Multiplier.

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Step-by-step explanation:

1/2×2 sin 5x. cosx

=1/2×sin (5x+x)+cos (5x-x)

=1/2 sin 6x +sin 4x

Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.

Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).

Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.

Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.

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The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

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The fraction of the package of raisins Ashley left with will be equal to 7/18.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Amount of raisins used for fruit cake = 1/2

Amount of raisins used for muffins = 1/9

Then, the amount of raisins left will be,

1 - (1/2 + 1/9)

= [18 - (9 + 2)]/18

= (18 - 11)/18

= 7/18

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The magnitude of vector is 8.24 and angle is 75.9638.

What is vector?

A vector could be a amount that not solely describes the magnitude however additionally describes the movement of an object or the position of an object with reference to another purpose or object.

Main body:

we know that the magnitude of vector is found out by,

| u | = [tex]\sqrt{i^{2}+j^{2} }[/tex]

so here , u = 2i + 8j

|u| = [tex]\sqrt{2^{2} +8^{2} }[/tex]

|u| = [tex]\sqrt{68}[/tex]

|u| = 8.24

now to find the direction , angle

tan∅ = j/k

tan∅ = 8/2

∅ = tan⁻¹ (4)

∅ = 75.9638°

Hence , direction angle of the following vector is ∅ = 75.9638°

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Continental glacier ice flows from the region where it is thickest toward the edges where it is thinner. In the central thickest parts, the ice flows almost vertically down toward the base, while at the edges of the glacier, it flows horizontally out toward the margins.

Glaciers generally advanced from the direction where the contour lines on the landforms are closest together (steep slope) toward the direction where the contour lines on the landforms are farther apart (gentle slope).

A continental glacier originating in far Northern Canada began to move South towards the Northeastern United States. The ice sheet crept slowly forward, scraping off the loose rock materials and gouging the bedrock beneath the ice as it advanced.

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This hypothesis is a false positive.

What is a false positive result?

When a scientist concludes something is real when it is actually wrong, this is known as a false positive (also called a type I error). A "false alarm" is a false positive. Saying something is false when it is truly true is known as a false negative (also called a type II error). A false negative indicates that something was missed or that something that was present was not discovered.

A false positive is getting a positive result that should be negative (this is also known as a “type I error”). A false negative is getting a negative result that should be positive (this is also known as a “type II error”).

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Answer:

  -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

Step-by-step explanation:

You want to simplify (7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3.

We recognize that there are some repeated expressions here that may make it easier to simplify this without multiplying it all out.

Let a = 7x+5y, b = 7x -5y. Then the expression becomes ...

  a³ -b³ -30y·a·b³

  = (a³ -b³) -30yb²(ab)

  = (a -b)(a² +ab +b²) -30yb²·ab

Now ...

  a -b = (7x +5y) -(7x -5y) = 10y

  a² +b² +ab = (7x +5y)² +(7x -5y)² +(7x +5y)(7x -5y)

     = (7x)² +2(7x)(5y) +(5y)² +(7x)² -2(7x)(5y) +(5y)² +(7x)² -(5y)²

     = 3(7x)² +(5y)² = 147x² +25y²

So the first pair of terms expands to ...

  a³ -b³ = 10y(147x² +25y²) = 1470x²y +250y³

The last term becomes (with a positive sign) ...

  30yb²(ab) = 30y(7x -5y)²((7x)² -(5y)²)

     = 30y((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) . . . . see comment below

     = 30y((7x)⁴ -(5y)⁴ -70xy((7x)² -(5y)²))

     = 72030x⁴y -18750y⁵ -102900x³y² +52500xy⁴

Putting it all together gives ...

  = -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

__

Additional comment

The difference of squares form is used several times here:

  p² -q² = (p -q)(p +q)

The expression ((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) is decomposed to ...

  ((7x)² +(5y)²)·((7x)² -(5y)²) - 2(7x)(5y)((7x)² -(5y)²)

This lets us use the difference of squares form to simplify at least part of the expression. This whole thing gets multiplied by -30y.

Answer: 19/7

Step-by-step explanation:

Your goal is to isolate x or get x by itself.

Move all other variables to the opposite side.

70x+10-10=200-10

70x=190

Divide both sides by 70

x= 19/7

Answer:

[tex]x= \frac{19}{7}[/tex]   OR   [tex]2 \frac{5}{7}[/tex]

Step-by-step explanation:

To do this you need to:

  1. Subtract 10 from both sides {As shown below}

[tex]70x+10-10=200-10[/tex]

  2. Simplify {As shown below}

[tex]70x=190[/tex]

   3. Divide both sides by the same factor {As shown below}

[tex]\frac{70x}{70} = \frac{190}{70}[/tex]

    4. Simplify {As shown below}

        {a. Cancel terms that are in both the numerator and the denominator}

        {b. Divide the numbers}

[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]

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The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.

The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.

To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

Step 1: Go to the chi-square distribution calculator.

Step 2: Enter the degrees of freedom, which is 10 in this case.

Step 3: Enter the confidence level, which is 99% in this case.

Step 4: Click the “Calculate” button.

Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

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