Explain how you could estimate 22% of 78 to check if your answer is reasonable.

If he  has allocated $67,050 for the cost of growing his crops. The number of acres of each crop that should  plant is Corn 270, Wheat 540, Soybeans 450.

Let c = corn

Let w = wheat

Let s = soybeans

C+W+S = 1260

45C + 60W + 50S = 67050

W =2C

Substitute equation 1 into equation 2

C + 2C +S = 1260

3C + S =1260

45C + 120C + 50S =67050

165C +50S =67050

Let eliminate S

165C+ 50(1260-3C) =67050

165C + 63000 - 150C= 67050

15C= 4050

Divide both side by 15c

c =4050/15

c = 270 (corn)

Wheat

W=2C

w = 2(270)

w= 540

S= 1260 - 3C

S= 1260- 3(270)

S =1260 -810

S = 450 (soybeans)

Therefore , 270, 540 and 450 are the acres that should be planted.

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The required greatest common factor is given as 6zx¹⁰t.

Given that,
To determine the greatest common factor among the expressions,

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,
Given expression,
=  6zx⁶tx⁴, 30zx⁸tx³, 18zx⁵tx⁵
Taking common 6zx¹⁰t,
= 6zx¹⁰t{1 , 5x³, 3}

Thus, the required greatest common factor is given as 6zx¹⁰t.

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Answer:A

Step-by-step explanation:

N is a lie, its increasing

Q is linear

R is linear

P must be true

Answer:

The answer is A) In Section P, the function is linear and increasing.

Step-by-step explanation:

B is false because it is not decreasing

C is false because it is considered linear (linear is a line). Non-linear is typically a curved line.

D is false because it's not increasing or decreasing, so when it states decreasing it isn't even right.

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a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is; P(2 ≤ X ≤ 5) = 0.8054

The formula for Binomial Probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

p is probability of success

n is number of trials

x = the number of expected successful outcomes

We are given;

p = 38% = 0.38

n = 10

Thus;

a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 10C2 * 0.38^(2) * (1 - 0.38)^(10 - 2)

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 1 - P(X ≤ 2)

P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is;

P(2 ≤ X ≤ 5) =  [P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

P(2 ≤ X ≤ 5) = 0.8054

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The fraction of a tank is used daily is 1/15.

Given that, Jordan uses 1/3 of a tank of gas each week on their commute for 5 days.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Average tank of gas used = Total tank of gas/Number of days

= 1/3 ÷ 5/1

= 1/3 × 1/5

= 1/15

Therefore, the fraction of a tank is used daily is 1/15.

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The viable solutions to the system will be (80, 90)

Gus is buying juice drinks, x, and snack packs, y, for a school picnic

The system of inequalities will be

x + y ≥ 150

1.5x + 3.5y ≤ 600

15x + 35y ≤ 6000

3x + 7y ≤ 1200.......equation 1

x + y ≥ 150....multiplied with 3

3x + 3y ≥  450...equation 2

3x + 7y - (3x + 3y) = 1200 - 450

3x + 7y - 3x - 3y = 750

4y = 750

y = 750/4

y ≤ 187.5

x + y ≥ 150.

x ≥ 150 - 187.5

x ≥ -37.5

Therefore, the viable solutions to the system will be (80, 90)

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The exact value of tan(F) in the simplest radical form for the given triangle is (√29)/8.

We are given a triangle. The vertices of the triangle are F, G, and H. The lengths of the sides of the triangle are given. The lengths of FG, GH, and HF are 8 units, √29 units, and √93 units, respectively. The triangle is a right-angled triangle. The measure of the angle ∠G is 90°. We must find the value of tan(F) in its most basic radical form. A radical expression is one that contains a square root.

Considering the angle ∠F, the base and the perpendicular of the triangle are FG and GH. The trigonometric ratio tan (F) is calculated as follows.

tan(F) = GH/FG

tan(F) = (√29)/8

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Examining the rainfall data for the two periods a conclusion is that the range of the values are period 1 has low variability while period 2 has high variability

period 1: 0.6

period 2: 4

The range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.

Measurements of variability provide you with descriptive statistics for summarizing your data set in addition to measures of central tendency.

By deducting the lowest value from the greatest value, the range is computed. A short range indicates low variability in a distribution, whereas a big range denotes significant variability.

The range is

period 1: 2.5 - 1.9 = 0.6

period 2: 4.7 - 0.7 = 4

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To solve for a variable, simply isolate it.

f + 32 = -2
f + 32 - 32 = -2 - 32
f = 34

Answer:

The correct answer is -34.

Answer: 1/8, Division equation: 1/3 divided by 8/3

Step-by-step explanation:

Step 1: Write this problem as an equation, of means multiply so the equation is 1/3 x 3/8.

Step 2: Solve the equation by multiplying the numerators and the denominators. You get 3/24.

Step 3: Simplify by dividing the numerator and denominator by their gcf. In this case it is 3. So, 1/3 of 3/8 is 1/8.

Step 4: Now we need to get the division equation of 1/3 x 3/8, for this you do the same thing as if we had to actually solve the division equation with fraction, just for changing multiplication to division instead. I am talking about keep change flip. You keep the first fraction the same. you change the operation to it's opposite ,and you flip the numerator and denominator in the second fraction. When we do this we get our division equation of 1/3 divided by 8/3.

JK and KL make up line JL.

JL = 2x + 8, JK = 2x - 2, KL = x - 9

If JK and KL make up line JL:

JK + KL = JL

We are solving for KL, so isolate it.

JK - JK + KL = JL - JK
KL = JL - JK
x - 9 = 2x + 8 - (2x - 2)
x - 9 = 2x - 2x + 8 + 2
x - 9 = 10

Often times, we would solve for x, but considering x - 9 is what we wanted the solution to anyway, we don't need to bother solving for x.

KL = 10

Answer: 20 tis it

Step-by-step explanation:

my man

The amount paid to vehicle A is less than to vehicle B so, Vehicle A is suitable to purchase based on a monthly payment.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

For vehicle A,

The Principal amount of the car, P = $25000,

The rate of interest, r = 5% = 5/100 = 0.05,

The tenure, n = 60 months = 60/12 = 5 years,

Calculate the amount by the formula given below,

A = P (1 + r)ⁿ

Here A is the amount,

Substitute the values,

A = 25000 (1 + 0.05)⁵,

A = $31907.03

Similarly,  for vehicle b

A = 29000 (1 +0.04)⁶

A = $36694.25

As the amount of vehicle A is less than the of vehicle B Therefore, vehicle A is suitable to buy.

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The phrase asked: [tex]\ln5\sqrt{55}[/tex]

if ln5=a and ln11=b:

 [tex]\ln5\sqrt{55} =\\\\ \ln5+\ln(55)^{\dfrac{1}{2}}=\\\\\\ \ln5+\dfrac{1}{2}(\ln55)=\\\\\\ \ln5+\dfrac{1}{2}(\ln5.11)=\\\\\\ \ln5+\dfrac{1}{2}(\ln5+\ln11)=\\\\\\ a+\dfrac{1}{2}(a+b)= \dfrac{1}{2}(3a+b)[/tex]

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

theorem 1:

[tex]\ln(x.y)= \ln x + \ln y[/tex]

theorem 2:

[tex]\log_a{x^n} = n \cdot \log_a{x}[/tex]

Answer:

x = 8. y = 21

Step-by-step explanation:

x + 8x + 18 = 90

combine like terms

9x + 18 = 90

-18 both sides

9x = 72

divide by 9 both sides

x = 8

______

3y + 27 = 90

-27 both sides

3y = 63

divide by 3 both sides

y = 21

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity,-4]

Step-by-step explanation:

infinity always has parentheses

domain is seen from left to right

range is seen from bottom to top

The probability that all a randomly chosen student has a schedule that excludes music theory, using the combination formula, is of:

p = 1/14.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Without simplifying it, the probability that all a randomly chosen student has a schedule that excludes music theory is of:

[tex]p = \frac{C_{4,3}}{C_{8,3}}[/tex]

The numeric value for each of these combinations is given as follows:

Hence the probability is given as follows:

p = 4/56.

The division of 56 by 4 has a quotient of 14, hence the simplified probability is of:

p = 1/14.

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The cups of flour required for 2 cups of cashew is 2.6667

The proportion given in the problem is 3 cups of cashews for 4 cups of flour.

From the given proportion we calculate for the quantity of flours required for 2 cups of cashew

3 cups of cashew = 4 cups of flours

2 cups of cashew = ?

cross multiplying

3 * ? = 4 * 2

? = 4 * 2 / 3

? = 8 / 3

? = 2.6667

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The result of adding the two given equations (-2x + 7y = -5 and -2x - 4y = 6) is -4x + 3y = 1

From the question, we are to determine the result of adding the two given equations.

The given equations are

-2x + 7y = -5 and -2x - 4y = 6

Now, we will add the equations

    -2x + 7y = -5

+ ( -2x - 4y = 6

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

-2x + (-2x) + 7y + (-4y) = -5 + 6

-2x - 2x + 7y - 4y = 1

Simplifying

-4x + 3y = 1

Hence, the result of adding the equations is -4x + 3y = 1

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Answer:30%

Step-by-step explanation:

Step-by-step explanation:

so,

100% = $130

1 % = 100%/100 = 130/100 = $1.30

the price changed by 169 - 130 = $39.

how many % are that ?

as many % and times 1% fits into $39 :

39 / 1.3 = 30%

the price increase was 30%.

Answer:

46/273

Step-by-step explanation:

To add fractions, they must have a common denominator. To set one, find a common multiple of both denominators. Simply multiply them together if it proves difficult.

7 x 39 = 253

Now set the denominators to this number and multiply the numerators by the opposite fraction's denominator.

39/259 + 7/253 = 46/253
This simplifies to 2/11

So, 1/3 + 1/39 = 2/11

Each  player will get 9 cards.

According to our question-

total people= 6

cards=52

52/6= 8.66

rounding off

=9

hence, each  player will get 9 cards.

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The values of f(2) = 0 & f(3) = 2.

Here given that,

f(0) = f(1) = 1

f(n+1) = (n)/(n-1)

We have to solve the equation if n = 1:

putting the value of n = 1 in the given equation f(n+1) = (n)/(n-1)

= f(1+1) = 1/(1-1)

= f(2) = 0

In the same way we have to solve the equation if n = 2:

putting the value of n = 2 in the given equation f(n+1) = (n)/(n-1)

= f(2+1) = 2/(2-1)

= f(3) = 2/1

= f(3) = 2

Hence the answer is the values of f(2) = 0 & f(3) = 2.

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Answer:

5+-

[tex]5 + - x {}^{2} [/tex]

[tex] - x {}^{2} + 5[/tex]

For function, f(-4)=20, f(0)=4, f(2)=16 and f(3)=26

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given function is

f(x)= { -4x +4 for x <= 0

{ 10x - 4 for x > 0

We need to find f(-4),f(0),f(2) and f(3)

f(-4) is -4x +4 as x<=0

-4(-4)+4

16+4=20

f(-4)=20

f(0) is -4x +4 as x<=0

-4(0)+4=4

f(0)=4

f(2) is 10x - 4 as x>0

10(2)-4

20-4

f(2)=16

f(3) is 10x - 4 as x>0

10(3)-4

30-4

f(3)=26

Hence f(-4)=20, f(0)=4, f(2)=16 and f(3)=26

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Answer:62

Step-by-step explanation:

let x=number of marbles Rasheed has
let 7x+6 = number of marbles Lacey has
x+7x+6=70
8x+6=70
8x=64
x=8
Plug 8 into 7x+6 and you get 62

Answer:

54

Step-by-step explanation:

40 x 135

_______

  100

=54

Answer: The probability that more than 12 of the entry forms will include an order is 0.624.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.

The probability that more than 12 of the entry forms will include an order can be found as:

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P( X = 3) - P(X = 4)

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

P(X > 4) = 1 - 0.0009 - 0.0097 - 0.043 - 0.117 - 0.205

P(X > 4) =  0.624

Thus, the probability that more than 12 of the entry forms will include order is 0.624.

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Step-by-step explanation:

Answer:

[tex] \huge{ \boxed{y = 4x + 10}}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is given by

[tex] \bold{y = mx + c}[/tex]

where

m is the slope

c is the y intercept

From the question

m = 4

In order to find c we substitute the point (−3,−2) into the equation y = mx + c

We have

[tex] - 2 = 4( - 3) + c \\ - 2 = - 12 + c \\ c = - 2 + 12 \\ c = 10[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = 4x + 10}[/tex]

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