f we start at the point (1,3,2), then in what direction should we move if we want to maximize the directional derivative?

After solving the expression, the number is 5.

In the given question we have to answer twice the sum of five times a number increased by one is twelve.

We have to determine the number by solving the given statement.

To solve the question we have to read the statement carefully. Then write the expression according to the statement. Then solve the statement according the rules.

In the given statement given that five time a number.

Let the number be x. So the expression should be 5x.

Again says that five times a number increased by one. So the expression 5x+1.

Then says that twice the sum of five times a number increased by one. Now the expression should be 2(5x+1).

Then says that twice the sum of five times a number increased by one is twelve. Now the statement is 2(5x+1)=12

Now solving the expression.

Divide by 2 on both side, we get

5x+1=6

Subtract 1 on both side, we get

5x=5

Divide by 5 on both side, we get

x=1

Now the number is 5.

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Answer:

61

Step-by-step explanation:

hope this helps

[tex]f(x)=(\dfrac{1}{4} )^x[/tex]

Please refer to the following graph below:

Answer:

x - 16 = -3

Step-by-step explanation:

x - 16 = -3  Add 16 to both sides of the equation

x = 13

It was 13 degrees at noon

$17505 must be deposited today.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Variable principal payments, or the portion of your mortgage payment that goes toward the loan itself rather than interest, are what give compound interest its feel.

Simple or compound interest are also possible. A loan's or deposit's initial principal serves as the foundation for simple interest.

Contrarily, compound interest is calculated based on both the principal amount and the interest that is accrued on it each period. Simple interest is simpler to calculate than compound interest because it is only applied to the principal.

According to our question-

In order to calculate compound interest, we would use the formula A = P(1+r/n)nt.

Where A = the account's total balance at the end of t years, and r is the interest rate.

The periodic interval at which it was compounded is represented by n.

P stands for the principal, or the initial deposit amount.

Since it was compounded once a year, A = 30000 r = 8% = 8/100 = 0.08 and n = 1 according to the information provided.

t = year

In light of this, 30000 = P(1 + 0.08/1)1 7 30000 = P(1.08)7 30000 = 1.7138P

P = 30000/1.7138 \s P = $17505

Hence, $17505 must be deposited today

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The mass of the Cougar is 70 Kg using the concept of equations.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It demonstrates the equal relationship between the expressions presented on the left and right sides. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved. If there is no "equal to" symbol, a statement is not an equation.

Let the mass of white-tailed deer = d

Mass of cougar = c

According to the question,

d = 1.4 × c                   ....(1)

d = 98 kg                   ....(2)

So,

1.4 × c = 98

c = 98/1.4

c = 70

So, the mass of the Cougar = 70 Kg

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Answer:

area of the isosceles triangle is [tex]60cm^{2}[/tex]

Step-by-step explanation:

three sides are a=10, b=13, c=13

Area of Triangle:

[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where,

[tex]s=\frac{a+b+c}{2}[/tex]

[tex]s=\frac{10+13+13}{2}[/tex]

s = 18

now,

[tex]A = \sqrt{18(18-10)(18-13)(18-13)}[/tex]

[tex]A =\sqrt{9(16)(5)(5)}[/tex]

A = 3x4x5

[tex]A =60cm^{2}[/tex]

The name of the property is transitive property if 3x= 4 and 4=z then 3 =z.

According to the transitive property, "if two quantities are equal to the third quantity, then we can claim that all quantities are equal to each other." The term transitive refers to the act of transferring something. If a, b, and c are three quantities and an is connected to b by some rule and b is related to c by the same rule, then a and c are related to each other by the same rule; this is known as the transitive property of equality.

The transitive property of equality states that if a = b and b = c for any values of a, b, and c, then a = c. In other words, because a and c are both equal to the same item (in this case, b), they must be equal as well.

Given,

3x=4 and 4=z then 3=z

Here a=3, b=4, c=z

The name of the property is transitive property

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The probability of choosing a person who owns a dog or a cat will be;

⇒ 0.845

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

Number of peoples in survey = 110

And, The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat.

Now,

Since, Number of peoples in survey = 110

And, Number of peoples owns a dog or a cat = 72 + 58 - 37

                                                                      = 93

Thus, The probability of choosing a person who owns a dog or a cat is,

Probability = 93 / 110

                = 0.845

Therefore, The probability of choosing a person who owns a dog or a cat will be;

⇒ 0.845

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Question 7

Using the secant-secant theorem,

[tex]4(x+4)=3(8) \\ \\ x+4=6 \\ \\ \boxed{x=2}[/tex]

Question 8

Using the intersecting chords theorem,

[tex]8(4x+2)=9(4x) \\ \\ 32x+16=36x \\ \\ 16=4x \\ \\ \boxed{x=4}[/tex]

1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³

An expression is combination of variables, numbers and operators.

Given expression is  1/2s−4+3/4s+1/8−s³

One by two times of s minus four plus three by four times of s plus one by eight minus s cube.

In the given expression minus, plus are the operators, s is the variable,

The expression has five terms

1/2s, -4, 3/4s, 1/8 and -s³ are the terms

Like terms contain the same variable which is raised to the same power.

In the given expression  1/2s and 3/4s are the like terms

Hence,  1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³

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The percent increase of his tips from Friday to Saturday is 35/3%.

T is equal to 112/3% as a mixed percentage fraction or 35/3% as an uncommon percentage fraction (decimal fraction: 0.116667)

PREMISES

T is the proportion of a waiter's tips that increased from $300 on Friday to $335 on Saturday.

CALCULATIONS

T=($335-$300)/$300

T=[($35/$300)100]%

T=[(7/60)100]%

T=[(7×100)/60]%

T=70/6%

A mixed percentage fraction of 112/3% or a percentage fraction of 35/3% (decimal fraction: 0.116667)

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The retail price of each video game is $33.6

From the question, we have the following parameters that can be used in our computation:

Markup rate = 40%

Amount paid = $24

The retail price of each video game can be calculated using the following equation

Retail price = Amount paid * (1 + Markup rate)

Substitute the known values in the above equation, so, we have the following representation

Retail price = 24 * (1 + 40%)

Evaluate

Retail price = 33.6

Hence, the retail price is $33.6

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Hence, the simplification is [tex]27-18i[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given equation is

[tex](-4+i)(-6+3i)[/tex]

then,

[tex]-4(-6+3i)+i(-6+3i)\\\\=24-12i-6i+3\\\\=24-18i+3\\\\=27-18i[/tex]

Hence, the simplification is [tex]27-18i[/tex].

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The ratio representing the number of votes for hot dogs to chicken is 2/5.

For the stated question.

Total votes = 20.

Pizza = 6

Chicken = 10

Hot dogs = 20 - 16 = 4

Then,

Ratio = votes for hot dogs/ votes for chicken

Ratio = 4/10

Ratio = 2/5

Thus, the ratio representing the number of votes for hot dogs to chicken is 2/5.

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The probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given: An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight.

The airline sells 170 tickets for a flight that has only 165 seats.

The proportion of reservations that do not show up for the flight

P = 5% =  0.05.

Number of tickets sold n = 170

Number of seats in the flight = 165

If at least 5 people do not show up then we have enough seats for every person.

P(X ≥ 5) =  Σ (from 5 to 170)[tex]170C_x(0.05)^x(0.95)^1^7^0^-^x[/tex]

P(X ≥ 5) ≈ 0.9306

Hence, the probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.

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the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

given that

the combined perimeter of a circle and square is 16cm

let side length of the square is s

let radius of the circle with r

So, the perimeter (P) and the area (A) of the shape are:

P= 4s + 2[tex]\pi[/tex]r

A = [tex]s^{2}[/tex] + [tex]\pi[/tex][tex]r^{2}[/tex]

given that perimeter is 16

so, 4s +2[tex]\pi[/tex]r = 16

divide by 4

s +0.5[tex]\pi[/tex]r = 4

s = 4 - 0.5[tex]\pi[/tex]r

substitute s value in area

A =  [tex](4-0.5\pi r)^{2}[/tex] + [tex]\pi[/tex]r

A = 16 - 4[tex]\pi[/tex]r +0.25[tex](\pi r)^{2}[/tex] +[tex]\pi[/tex][tex]r^{2}[/tex]

A =16 - 4[tex]\pi[/tex]r + (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])[tex]r^{2}[/tex]

differentiate with respect to r

A' = 0 - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r

A' = - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r

now A' =0

- 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r =0

2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r =  4[tex]\pi[/tex]

divide both sides by 2

(0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r = 2[tex]\pi[/tex]

r = [tex]\frac{2\pi }{0.25\pi ^{2} +\pi }[/tex]

r = [tex]\frac{2\pi }{\pi (0.25\pi +1)}[/tex]

substitute  [tex]\pi[/tex] =3.14

r = 2/(0.25(3.14)+1)

r = 1.12

substitute r value in s

s = 4 - 0.5 * 3.14 *1.12

s =2.24

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

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Answer: -2 1/3

Step-by-step explanation:

Okay

Answer: $0.14

Step-by-step explanation: All we have to do is divide $1.12 by 8 to get our answer, that being $0.14.

The required hypothesis are as follows , H0: μ = 438 and Ha: μ ≠ 438

The null hypotheses for the above scenario will be the statement of no effect and it'll be the mean weight of the bag that filled will be 438grams.

H0: μ = 438

The alternative hypotheses for the above scenario will be that the bag isn't filled with 438grams. They are either underfilled below 438grams or overfilled above 438grams.

Ha: μ ≠ 438

Statistics is the study of surveys and research on numerical data. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.

The null hypothesis is a broad assertion or default condition that there is nothing happening. For instance, there is no relationship between two measured occurrences or a connection between groups.

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Answer:

69.29 deg

Step-by-step explanation:

Recall that tan(x) = opposite/adjacent. This is helpful because we know the opposite and adjacent leg from the angle x! This gives us tan(x) = 43/18, so we can solve for x by taking tan^-1 of both sides, giving x = tan^-1(43/18), or 67.29 degrees.

rhambus has four equal sides

so r+l=2r-4

r=5

b-3=r+l=6

b=9

Diamond adjacent angle complementation

So (x+2x+6)=180*

3x=174

x=58

All in all r=5 b=9 x=58 4b-6r=21-4=r+l=b-3=6

2x+6=122

this is the answer thank you when you have th problem you can tell me

Answer:

 check the attached file

Step-by-step explanation:

Pairs 1 &2 are not similar whereas pairs 3&4 are similar.

The term "similarities" refers to pairs of objects whose corresponding sides have the same ratio. When two figures, such as the rectangles A and B, are given:

length A/length B equals width A/width B

We enter the values of the pairs in the formula above to determine which pairs are similar:

Pair 1

169/1.3=130

49/0.7=70

130 ≠70

therefore the first pair is not similar

Pair 2

18.55/5.3=3.5

10.5/3.5=3

Pair 2 is not similar

Pair 3

120/24=5

60/12=5

this implies that pair 3 is similar

Pair 4

189/2.1=90

81/0.9=90

this means that pair 4 is similar.

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Answer:

(1,16),(2,32),(3,48),(4,64)

Step-by-step explanation:

so 1=16

2×16=32

3×16=48

4×16=64

The correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)

For this equation we have to "multiply" each number that makes scene.

We got to work with what is given in the question.

Given options:

(16, 1), (32, 2), (48, 3), (64, 4)

(1, 16), (2, 32), (3, 48), (4, 60)

(1, 16), (2, 32), (3, 48), (4, 64)

(1, 32), (2, 48), (3, 64), (4, 80)

Therefore, the equation is:

[tex]2*16\\3*16\\4*16[/tex]

Therefore, the correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)

The probability of committees contain 2 boys and 1 girl is 9.

In the given question,

A committee of 3 is selected from Jillian, Miles, Mark, and Nikia.

We have to find the how many committees contain 2 boys and 1 girl.

As we know that,

Simply put, probability is the likelihood that something will occur. If we don't know how such an occurrence will end out, we can discuss the possibility or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

There are total 3 selection.

Possibility of selecting 2 boys = [tex]^{3}C_{2}[/tex].

There are total 3 selection.

Possibility of selecting 1 girl = [tex]^{3}C_{1}[/tex].

So the probability of committees contain 2 boys and 1 girl is

P(C) = [tex]^{3}C_{2}\times^{3}C_{1}[/tex]

After solving

P(C) = 9

The probability of committees contain 2 boys and 1 girl is 9.

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Answer:

Below

Step-by-step explanation:

base * height = volume

volume / base = height

divide 10x^2-9x+2    INTO   10x^3 + 21x^2 MINUS 25x +6

                                             ( you left out the minus sign in your post)

to get height = x+3

We know that 68.26% of data is between 580 and 620 using a normal distribution table.

A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution.

Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.

So, we know that:

μ = 600

σ = 20

Use the equation:
z - score = x-μ/σ

580 in the data's Z-score:

= 580-600/20

= -20/20

= -1

While the data's z-score in 620:

= 620-600/20

= 20/20

= 1

Using a table of the normal distribution:

P(580 < z) = 0.1587

Also, P(620 > z) = 0.8413

As a result, the percent of the data that falls between 580 and 620 is given by: P(620 > z) - P(580 z).

= 0.8413  - 0.1587

= 0.6826

= 68.26 %

Therefore, we know that 68.26% of the data is between 580 and 620 using a normal distribution table.

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Answer:

5:8

Step-by-step explanation:

The ratio of dogs and cats is 5:8

The ratios always have a common multiple.

Let that common multiple is ‘a’

So dogs and cat are:

dogs=5a

cats=8a

total animals=5a+8a=13a

13a=52

a=52/13

= 4 ——- Means, the common multiple is ‘4’

So, number of cats = 8a

=8*4=32

Answer:

37

Step-by-step explanation: