example of perpendicular lines

Answer:

One ounce of almonds is $0.78

One ounce of cashews is $0.63

Step-by-step explanation:

Set up a system of equations where a is the price of one ounce of almonds and c is the price of one ounce of cashews:

20a + 12c = 23.16

18a + 14c = 22.86

Solve by elimination by multiplying the top equation by 7 and the bottom equation by -6:

140a + 84c = 162.12

-108a - 84c = -137.16

Add them together and solve:

32a = 24.96

a = 0.78

Now, plug in 0.78 for a and solve for c:

20a + 12c = 23.16

20(0.78) + 12c = 23.16

15.6 + 12c = 23.16

12c = 7.56

c = 0.63

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

13:2

Step-by-step explanation:

26 to 24 = 26/24 can further be simplified to 13/12

13/12 = 13:12

Plz mark as brainliest, I am close to expert.

A) The appropriate hypothesis test to determine if there is a statistically significant association between sales and profits is B. H_0: There is no linear relationship between sales and profits, beta_1 = 0. H_A:

There is a linear relationship between sales and profits, beta_1 ≠ 0. This test will determine if there is a linear relationship between the two variables, regardless of the direction of the relationship (positive or negative).

B) The conclusion of this test would be based on the p-value obtained from the test. If the p-value is less than the significance level of 0.05, we would reject the null hypothesis and conclude that there is a statistically significant linear relationship between sales and profits.

If the p-value is greater than 0.05, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a linear relationship between the two variables.

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Answer:

answers in the explanation cz I'm too lazy to type :(

not entirely sure tho

Step-by-step explanation:

w²+2w-42=0

*quadratic formula*

w= -1+ square root 43 m

or w= -1- square root 43 m

then since the length is 2m more than w

add 2 to both answers

l= 1+ square root 43 m

l=1- square root 43 m

9514 1404 393

Answer:

Step-by-step explanation:

Given:

  a rectangular patio of width w meters, length w+2 meters, and area 42 m²

Find:

  width and length

Solution:

The area is ...

  A = LW

  42 = w(w +2)

  43 = w² +2w +1 . . . . . . add 1 to complete the square

  √43 = w+1

  w = √43 -1 ≈ 5.557 . . . meters

  l = w+2 = √43 +1 ≈ 7.557 . . . meters

The width and length of the patio are 5.557 m and 7.557 m, respectively.

Answer:

TOTAL AMOUNT=$1300

interest =30.13%

Step-by-step explanation:

\(total amount =Deposit+ MP\\TA= 100+(100*12)\\TA=1300\\Interest= \frac{1300-999}{999}*100= 30.13\)

Answer:

10 In the diagram below, DE divides AB and AC proportionally, m∠C = 26°, m∠A = 82°, and DF bisects ∠BDE. The measure of angle DFB is. 1) 36°. 2) 54°. 3) 72°.

Step-by-step explanation:

The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer:

1. Number of boys in A is 52028.

2. Number of girls in B is 46510.

3. Town B has more number of girls.

Step-by-step explanation:

1. \(95364 - 43336 = 52028\)

2. \(100005-53495=46510\)

3. \(43336<46510\) (A < B)

Answer:

the answer should be 158 but I'm not a hundred percent sure

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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Answer:

option 1

Step-by-step explanation:

Answer: 34,650 permutations

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

y = -x + 8

Step-by-step explanation:

Let's break down the equation step by step to understand it better.

The equation in point-slope form is given as:

y - y1 = m(x - x1)

In this case, we have:

y - 0 = -1(x - 8)

The point-slope form uses a specific point (x1, y1) on the line and the slope (m) of the line.

Here, the point (x1, y1) is (8, 0), which represents a point on the line. This means that when x = 8, y = 0. The graph has a point at (8, 0), which confirms this information.

The slope (m) is -1 in this equation. The slope represents the rate at which y changes with respect to x. In this case, since the slope is -1, it means that for every unit increase in x, y decreases by 1. The negative sign indicates that the line has a downward slope.

By substituting the values into the equation, we get:

y - 0 = -1(x - 8)

Simplifying further:

y = -x + 8

This is the final equation of the line in slope-intercept form. It tells us that y is equal to -x plus 8. In other words, the line decreases by 1 unit in the y-direction for every 1 unit increase in the x-direction, and it intersects the y-axis at the point (0, 8).

If the graph has points at (0, 8) and (8, 0), the equation y = -x + 8 accurately represents that line.

Answer:

x=13.45

Step-by-step explanation:

This is a right triangle. We know this because of the little square in the corner that represents a right angle. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse.

In this triangle, 10 and 9 are the legs, because they form the right angle. x is the hypotenuse, because it is opposite the right angle.

a=10

b=9

c=x

Substitute these values into the equations.

10^2+9^2=x^2

Evaluate the exponents on the left side.

10^2=10*10=100

100+9^2=x^2

9^2=9*9=81

100+81=x^2

Add 100 and 81

181=x^2

Since x is being squared, take the square root of both sides. The square root and the exponent will cancel, and leave x by itself.

√181=√x^2

√181=x

13.4536240471=x

Round to the nearest hundredth. The 3 in the the thousandth place tells us to leave the 5 in the hundredth place as is.

13.45=x

The hypotenuse of the triangle is 13.45

SOLUTION

From the given figure,

Since the triangle are similar it follows:

Solve the equation for x

Therefore the height of the tree is 60 ft

Answer:

  503.9 ft

Step-by-step explanation:

The geometry of the problem can be represented by a right triangle with one known leg, one unknown leg, and an acute angle adjacent to the known leg. The trigonometric function tangent is used to relate these measures:

  Tan = Opposite/Adjacent

  tan(27°) = height/(989 ft)

Multiplying by the denominator, we find ...

  height = (989 ft)tan(27°)

  height ≈ 503.9 ft

The balloon's vertical distance from the ground is about 503.9 feet.

Answer:

1) 2x+4(x-1)= 2+4x = x = 3

2) 25 - x = 15 - (3x + 10) = x = -10

3) 4x = 2x + 2x + 5(x-x) = x = any value of x make the equation true

Step-by-step explanation:

1) 2x+4x-4=2+4x

6x-4=2+4x

6x-4+4=2+4x+4

6x=4x+6

6x-4x=4x+6-4x

2x=6

2x/2 = 6/2

x= 3

2) 25-x=-3x+5

25-x-25=-3x+5-25

-x=-3x-20

-x+3x=-3x-20+3x

2x=-20

2x/2 = -20/2

x= -10

Answer:

y = 8

Step-by-step explanation:

\( \frac{5y}{4} = 10\)

\( \frac{4}{5} \times \frac{5y}{4} = \frac{4}{5} \times 10\)

\( \frac{1}{5} \times 5y = \frac{4}{5} \times 10\)

\(y = \frac{4}{5} \times 10\)

\(y = 4 \times 2\)

\(\boxed{\green{y = 8}}\)

Answer:

y=8

Step-by-step explanation:

We move all terms to the left:

5y/4-(10)=0

We multiply all the terms by the denominator

5y-10*4=0

We add all the numbers together, and all the variables

5y-40=0

We move all terms containing y to the left, all other terms to the right

5y=40

y=40/5

The researcher claim is invalid and the p-value based on alpha = 0.05 is   approx. = 0.

In the question ,

it is given that ,

a researches claims that per person yearly consumption (μ) is 52 gallons .

sample size (n) = 50 .

the mean of the consumption (x) = 56.3 .

the standard deviation (σ) is = 3.5 gallons .

the α = 0.05 .

let the null hypothesis ,

H₀ : μ = 52 and

H₁ : μ ≠ 52 .

the test statistics is : z = (x - μ)/(σ/√n)

the critical value ( rejection region ) : {z : |z| ≥ z₀.₀₂₅ = 1.96 }

So , z = (56.3 - 52)/(3.5/√50)

Simplifying further ,

we get ,

z = 8.69

We reject the null hypothesis H₀ , since the absolute value of the test statistics 8.69 is greater than the critical value 1.96 .

Since this is a two tailed test,  p-value must be multiplied by two

2 × P(z > 8.69) ≈  0

Since the p-value is less than α(0.05), So ,we reject the claim of the researcher that the mean yearly consumption of soft drinks per person is 52 gallons

Hence , the claim is not valid .

Therefore , The claim is invalid and p-value is ≈ 0 .

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P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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The statement "As2C__CERR" can be completed by adding either "O" or "S" between the two carbon atoms "As2CO" and "As2CS"  to make a valid chemical formula.

"As2CO" represents the compound dicarbonyl di-σ-carbon, which has two carbon atoms bonded by two double bonds and two oxygen atoms, while "As2CS" represents the compound bis(σ-carbene) diarsene, which has two carbon atoms bonded to two arsenic atoms by two double bonds.

Therefore, both "O" and "S" can be placed in the blank to make the statement true, since they represent valid chemical formulas for different compounds.

In summary, the answer to the question is "Both C & CO" since both "As2CO" and "As2CS" are valid compounds that can be formed by adding either "O" or "S" between the two carbon atoms in the given statement. This is an example of how the placement of different atoms or molecules in a chemical formula can result in distinct compounds with different properties and applications.

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Answer:

$38.4

Step-by-step explanation:

She leave a 20% tip -> she leave 20% x $32 = $6.4

In total, she paid : 32 + 6,4 = 38,4 for the ride.

Answer: 1085

Step-by-step explanation:

3n=n-2

3n-n=2

2n=2

n=1

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Answer:

6

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-(-2) is equal to +2, so the equation is 3+2 which is 5