A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans to use two different trucking firms. Big Red has heavy-duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on transportation. The availability of trucks is the same for both firms.

Answer:

The solution of the equation is Ф = 0 or Ф = 3π/2

Step-by-step explanation:

* Lets revise some facts in trigonometry

- The identity sin² Ф + cos² Ф = 1

- By subtracting sin² Ф from both sides then cos² Ф = sin² Ф - 1

- In the rectangular plane the point (x , y) represents  (cos Ф , sin Ф)

 where x = cox Ф and y = sin Ф

- The point (1 , 0) lies on the positive part of x-axis means cos Ф = 1

 and sin Ф = 0, then Ф = 0 or 2π

- The point (-1 , 0) lies on the negative part of x-axis means cos Ф = -1

 and sin Ф = 0, then Ф = π

- The point (0 , 1) lies on the positive part of y-axis means cos Ф = 0

 and sin Ф = 1, then Ф = π/2

- The point (0 , -1) lies on the negative part of y-axis means cos Ф = 0

 and sin Ф = -1, then Ф = 3π/2

* Lets solve the problem

∵ sin Ф + 1 = cos² Ф

- To solve we must change cos² Ф to sin² Ф

∵ cos² Ф = sin² Ф - 1

- substitute cos² Ф in the equation by 1 - sin² Ф

∴ sin Ф + 1 = 1 - sin² Ф ⇒ add sin² Ф to both sides

∴ sin² Ф + sin Ф + 1 = 1 ⇒ subtract 1 from both sides

∴ sin² Ф + sin Ф = 0

- Take sin Ф as a common factor from both terms

∴ sin Ф (sin Ф + 1) = 0

- Equate each factor by 0

∴ sin Ф = 0 OR sin Ф + 1 = 0

- Remember 0 ≤ Ф < π

∵ sin Ф = 0 ⇒ from the information above

∴ Ф = 0

∵ sin Ф + 1 = 0 ⇒ subtract 1 from both sides

∴ sin Ф = -1

- From the information above

∴ Ф = 3π/2

* The solution of the equation is Ф = 0 or Ф = 3π/2

Answer:

4 hours at 8 miles an hour: 8(4) = 32 miles in total

8 hours at 2 miles an hour: 2(8) = 16 miles in total

Miles in total: 32 + 16 = 48

The answer is A. 48 miles

Answer: 48

Step-by-step explanation:

8 (MPH) x 4 (H) = 32 miles covered in 8 hours.

2(MPH) x 8 (H) = 16 miles covered in 8 hours.

32 + 16 = 48 MPH

Answer:

No, the answer is actually a) 962

Step-by-step explanation:

Answer:

[tex]x=0[/tex]

[tex]y=-7[/tex]

Step-by-step explanation:

Let's use elimination.

We can multiply the second equation by -2 so that we can eliminate one variable from the system of equations.

[tex]-2(y=x-7)[/tex]

[tex]-2y=-2x+14[/tex]

Now we can use elimination and subtract.

[tex]y=2x-7[/tex]

[tex]-2y=-2x+14[/tex]

[tex]-y=7[/tex]

[tex]y=-7[/tex]

Now we can plug in the value of y into the first equation.

[tex]-7=2x-7[/tex]

[tex]2x=0[/tex]

[tex]x=0[/tex]

We can plug these values to check.

[tex]-7=0-7[/tex]

[tex]-7=0-7[/tex]

Answer:

Option (C): 8x^4yz^4√2yz

Step-by-step explanation:

Math. Give me Brainliest please?

Answer:

y-7=-(5/3)(x+3)

Step-by-step explanation:

step 1

Find the slope of the line that is perpendicular to 3x-5y=80

we have

3x-5y=80

5y=3x-80

y=(3/5)x-16

The slope of the given line is m1=3/5

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

m1*m2=-1

Find m2

(3/5)*m2=-1

m2=-5/3

step 2

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-5/3

point (-3,7)

substitute

y-7=-(5/3)(x+3) ----> equation of the line into point slope form

Answer:

a line that might best estimate the data and be used for predicting values.

Choice B is correct

Step-by-step explanation:

A line of fit might be defined as;

a line that might best estimate the data and be used for predicting values.

This line connects most of the data points thus minimizing the squared residuals of the regression.

I hope this helps...

Answer:

A line of fit might be defined as:

b)  a line that might best estimate the data and be used for predicting values.

Step-by-step explanation:

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Line of best fit is actually a good approximation of data and is used to predict values on the graph.

Answer:

Step-by-step explanation:

A double-blind study is a study where neither participants nor experimenters know which subjects are receiving the treatment.

This method is really useful to minimize possible biased conclusions about the experiment.

Therefore, the right answer is C, the situation described refers to a double-blind study.

A double-blind study is an experimental design in which both the subjects and experimenters are unaware of the treatment or control group assignments, thereby reducing bias and increasing the reliability of the study's findings.Therefore, the correct answer is option C.

An experiment where neither the subjects nor the experimenters know which subjects are in the treatment or control group is best described as a double-blind study.

This type of research design is crucial to prevent biases from affecting the outcome of clinical trials or other medical studies. In a double-blind study, both the participants and researchers are 'blind' to the assignments, thereby reducing the risk of placebo effects or experimenter bias influencing the results.

Experiments in the field of medicine often use this design to test the efficacy of new drugs, treatments, or interventions in the most unbiased way possible.

A control group that receives a placebo is essential in these experiments to compare the actual efficacy of the experimental treatment against no treatment or a standard treatment.

Answer:

126.

Step-by-step explanation:

Using long division:

        1 2 6

       ---------

36 ) 4536

       36

       ---

         93

          72

          ---

          216

          216

           ----

Answer:

126

Step-by-step explanation:

you divide 4536 and 36 and you get 126 as your quotient

Answer:

Midpoint D (-a-b , c)

Third option

Step-by-step explanation:

Midpoint D

x = 1/2 (-2a - 2b) = -a - b

y = 1/2 (2c) = c

Midpoint D (-a-b , c)

Answer:  (-a-b, c)

Step-by-step explanation:

We know that the mid point of a line having endpoints [tex](x_1,y_1)[/tex] and  [tex](x_2,y_2)[/tex]  is given by :-

[tex]x=\dfrac{x_1+x_2}{2}\ , \ y=\dfrac{y_1+y_2}{2}[/tex]

In the given figure it can be seen that D is the midpoint of RT :

Since R(-2b , 2c)  and  T(-2a, 0)

Then , the midpoint D of a line having endpoints [tex](-2b,2c)[/tex] and  [tex](-2a,0)[/tex] is given by :-

[tex]x=\dfrac{-2b+(-2a)}{2}=\dfrac{2(-a-b)}{2}=-a-b\ , \ y=\dfrac{2c+0}{2}=c[/tex]

Hence , the coordinates of midpoint D = (-a-b, c)

Answer:36

Step-by-step explanation:

The given parameters include;

The time to complete each trip is calculated as;

distance =[tex]speed $\times$ time[/tex]

forward distance = backward distance

[tex]&20 x=16 x+6 \\[/tex]

[tex]&20 x-16 x=6 \\[/tex]

[tex]&4 x=6 \\[/tex]

[tex]&x=\frac{6}{4} \\[/tex]

[tex]&x=1.5 h r[/tex]

The total time of the motion for the entire trip exists calculated as follows;

Time = time for forward + time for backward

[tex]\text { time } &=1.5 \mathrm{hr} r_{\text {forward }}+1.5 \mathrm{hr} \text { backward }+\frac{6 \mathrm{mi}}{16 \mathrm{mi} / \mathrm{hr}} \text { backward } \\[/tex]

time [tex]&=2(1.5) \mathrm{hr}+0.375 \mathrm{hr} \\[/tex]

time[tex]&=3.375 \mathrm{hr}[/tex]

The time for the entire trip is 3.375 hours.

The total distance of the trip exists calculated as follows;

total distance = forward distance + backward distance total distance [tex]$=20 \times 1.5+16 \times 1.5+6$[/tex] miles

Total distance =60 miles

Therefore, the total distance of the trip is 60 miles.

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Answer:

The wide of river is [tex]50\ ft[/tex]

Step-by-step explanation:

In this problem we know that

Triangles DEG and DEF are congruent by ASA (Angle-Side-Angle) Congruence

therefore

EG=EF

[tex]EG=20*(2\frac{1}{2})=20*\frac{5}{2}=50\ ft[/tex]

Answer:

[tex]8(x+10)[/tex]

Step-by-step explanation:

we have the expression

[tex](8x+80)[/tex]

we know that

[tex](8x+80)=(8x+8(10))[/tex]

Factor the number 8

[tex](8x+8(10))=8(x+10)[/tex]

therefore

The expression factored is [tex]8(x+10)[/tex]

The factorization of the given expression is given as:

                                 [tex]8(x+10)[/tex]

To factor a algebraic equation means to represent it as the multiplication of the simple expressions.

( i.e. if the expression has a common multiple in each of the terms then we take  it out and represent the rest of the expression in brackets.

Also, we can express a algebraic equation by the multiplication of the factors of the expression )

We are given a expression as:

[tex]8x+80[/tex] which represents  the total amount in the account after 8 months.

and x represents the amount saved each month.

Since both the terms i.e. 8x and 80 have a common multiple as: 8

Hence, we take it out of the expression and write the resulting expression as follows:

[tex]8x+80=8(x+10)[/tex]

Answer:

B) symmetric

Step-by-step explanation:

We will find the sample space for rolling two dices first

Here first value in ordered pair represents yellow die and second represents blue die

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

The subtraction gives us:

0 , -1 , -2, -3, -4, -5, 1, 0, -1, -2, -3, -4, 2, 1, 0, -1, -2, -3, 3, 2, 1, 0, -1, -2, 4, 3, 2, 1, 0, -2, 5, 4, 3, 2, 1, 0

So the distribution will be as follows:

X      5       4       3       2        1        0        -1       -2      -3       -4      -5

P(X)  1/36  2/36  3/36 4/36  5/36  6/36  5/36  4/36  3/36  2/36  1/36

By observing the probabilities, we can conclude that the distribution will be symmetric

Hence, Option B is correct ..

Answer:

its B symmetric

Step-by-step explanation:

got it right on ed

[tex]|8x-4|\leq12\\4|2x-1|\leq12\\|2x-1|\leq3\\2x-1\leq3 \wedge 2x-1\geq-3\\2x\leq 4 \wedge 2x\geq-2\\x\leq 2 \wedge x\geq-1\\x\in \langle -1,2\rangle[/tex]

The solution set of the inequality |8x-4| ≤ 12 is [-1, 2]. The solution was found by breaking down the absolute value into two separate inequalities and solving them.

To solve the inequality |8x-4| ≤ 12, we use the property that |a| ≤ b is equivalent to -b ≤ a ≤ b. So, the inequality can be rewritten as -12 ≤ 8x-4 ≤ 12. We then solve these two inequalities separately.

For -12 ≤ 8x-4, first add 4 to both sides to get -8 ≤ 8x, then divide by 8 on both sides to get x ≥ -1.

For 8x-4 ≤ 12, add 4 to both sides to get 8x ≤ 16, and then divide by 8 on both sides to get x ≤ 2.

Since x has to satisfy both these inequalities, the solution set is x ≥ -1 and x ≤ 2. In interval notation, this is represented as [-1, 2].

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Answer:

(-1,-2)

Step-by-step explanation:

y=ax^2+bx+c

Find -b/(2a) and you will have found the x-coordinate of the vertex of this parabola.

You can find the y-coordinate that corresponds to it by plugging in your into the original equation.

-b/(2a)=-6/(2*3)=-6/6=-1

Now replace x with -1

3(-1)^2+6(-1)+1

3-6+1

-3+1

-2

So the vertex is (-1,-2)

Answer:

Factor out a -1 from one of the terms so they are the same

Step-by-step explanation:

15x^2 – 3x – 20x + 4

(15x2 – 3x) + (–20x + 4)

3x(5x – 1) + 4(–5x + 1)

Talia should notice that the terms in the parentheses are opposites of each other and factor out a -1 out of the second term

3x(5x-1) +4 (-1) (5x-1)

Now the terms have a common factor

(5x-1) (3x+(-1)4)

(5x-1) (3x-4)

Answer:

Talia needs to factor out a negative from one of the groups so the binomials will be the same.

Step-by-step explanation:

[tex]15x^2 - 3x - 20x + 4[/tex]

Group first two terms and last two terms to factor it

[tex](15x^2 - 3x)+(- 20x + 4)[/tex]

Now we factor out GCF

GCF of 15x^2-3x is 3x

GCF of -20x+4 is -4 because first term should be positive

[tex](15x^2 - 3x)+(- 20x + 4)[/tex]

[tex]3x(5x- 1)-4(5x-1)[/tex]

Talia needs to factor out negative so that the binomials will be same (5x-1)

For this case we must solve the following equation:

[tex]-3 (h + 5) + 2 = 4 (h + 2) -9[/tex]

We apply distributive property to the terms of parentheses:

[tex]-3h-15 + 2 = 4h + 8-9[/tex]

We add similar terms:

[tex]-3h-13 = 4h-1[/tex]

We add 13 to both sides of the equation:

[tex]-3h = 4h-1 + 13\\-3h = 4h + 12[/tex]

Subtracting 4h on both sides of the equation:

[tex]-3h-4h = 12\\-7h = 12\\h = - \frac {12} {7}[/tex]

ANswer:

[tex]h = - \frac {12} {7}[/tex]

Answer:

[tex]h=-\frac{12}{7}[/tex]

Step-by-step explanation:

To solve the equation for h follow the next steps

[tex]-3(h+5)+2=4(h+2)-9[/tex]

Subtract 4(h+2) on both sides of the equality

[tex]-3(h+5)+2-4(h+2)=4(h+2)-4(h+2)-9[/tex]

[tex]-3(h+5)+2-4(h+2)=-9[/tex]

Subtract 2 on both sides of the equality

[tex]-3(h+5)+2-4(h+2)-2=-9-2[/tex]

[tex]-3(h+5)-4(h+2)=-11[/tex]

Apply the distributive property

[tex]-3h-15 -4h-8=-11[/tex]

[tex]-7h-15 -8=-11[/tex]

[tex]-7h-23=-11[/tex]

Sum 23 on both sides of equality

[tex]-7h-23+23=-11+23[/tex]

[tex]-7h=12[/tex]

Divide by -7 on both sides of the inequality

[tex]\frac{-7}{-7}h=-\frac{12}{7}[/tex]

[tex]h=-\frac{12}{7}[/tex]

Answer:  [tex]y=\frac{1}{30}x+1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

You need to find slope of the line with the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula:

 [tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

[tex]b=1[/tex]

Substituting the slope and the y-intercept found into  [tex]y=mx+b[/tex], you get the equation of this line:

 [tex]y=\frac{1}{30}x+1[/tex]

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

Step-by-step explanation:

7(x + 6) = 42

distributive property:  a(b + c) = ab + ac

(7)(x) + (7)(6) = 42

7x + 42 = 42

subtraction property of equality  (subtract 42 from both sides)

7x + 42 - 42 = 42 - 42

7x = 0

division property of equality   (divide both sides by 7)

7x : 7 = 0 : 7

x = 0

Answer:

1. Distributive property: a(b + c) = a.b + a.c

2. Property of subtraction of equality

3. Property of division of equality

Step-by-step explanation:

The given equation is 7x + 42 = 42

7(x+6)=42    [Distributive property: a(b + c) = a.b + a.c]

7x+42=42   [Property of subtraction of equality]

Subtract 42 from both sides.

7x + 42 - 42 = 42 - 42

7x=0  

Property of division of equality

Divide both sides by 7.

x=0

Answer:

156.429

Step-by-step explanation:

52.1428571 in one year x 3

Remember:

SOH-CAH-TOA

(Sine = [tex]\frac{opposite}{hypotenuse}[/tex] - Cos = [tex]\frac{adjacent}{hypotenuse}[/tex] - tan = [tex]\frac{opposite}{adjacent}[/tex])

For angle H the sin ratio is...

side FG (5) is opposite angle H

side HF (13) is the hypotenuse

so...

sinH = [tex]\frac{5}{13}[/tex]

For angle F the sin ratio is...

side HG (12) is opposite angle F

side HF (13) is the hypotenuse

so...

sinF = [tex]\frac{12}{13}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex] should be used to find b.

Step-by-step explanation:

We are given that in a triangle ABC, ∠A = 35°, ∠B = 40° and side a = 9 and we are to find the side length b.

Now using sine rule to find b:

[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex]

[tex]\frac{sin 40}{b} = \frac{sin 35}{9}[/tex]

[tex]b=\frac{sin 40 \times 9}{sin 35}[/tex]

b = 10.1

Answer:

The equation is 9/sin(35) = b/sin(40) , The length of b = 10.086

Step-by-step explanation:

* Lets explain how to solve the triangle

- In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- m∠A = 35°  

- m∠B = 40°  

- a = 9  ⇒ the side opposite to angle A

* To solve the triangle we can use the sin Rule

- In any triangle the ratio between the length of each side  

 to the measure of each opposite angle are equal

- a/sinA = b/sinB = c/sinC

∴ The equation which used to find b is a/sinA = b/sinB  

∵ a = 9 , m∠A = 35° , m∠B = 40°

∴ 9/sin(35) = b/sin(40) ⇒ by using cross multiplication

∴ b = 9 × sin(40) ÷ sin(35) = 10.086

* The length of b = 10.086

Answer:

(- 4, - 10 )

Step-by-step explanation:

Given the 2 equations

y = x - 6 → (1)

x = - 4 → (2)

Substitute x = - 4 into (1) for corresponding value of y

y = - 4 - 6 = - 10

Solution is (- 4, - 10 )

Answer:

the answer is b (-4,-8)

Step-by-step explanation:

i got it right top one is wrong

Answer:

x = 2

Step-by-step explanation:

Using the rules of logarithms

• log x + log y ⇔ log(xy)

• log [tex]x^{n}[/tex] ⇔ n log x

• log x = log y ⇔ x = y

Given

3ln2 + ln8 = 2ln(4x)

ln 2³ + ln8 = ln(4x)²

ln8 + ln8 = ln 16x²

ln(8 × 8) = ln 16x²

ln 64 = 16x², hence

16x² = 64 ( divide both sides by 16 )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

Answer:

[2x + 1\5] + ⅜

Step-by-step explanation:

Simply combine like-terms, then evaluate.

Answer:

1) If 3 is an odd number, then 3 times 3 is an even number.

False because multiplying odd number by an odd number also gives an odd number.

2) If 6 is less than 7, then 4 is greater than 7.

False because 4 is smaller than 6. As 6 is smaller than 7 then 4 must also be smaller.

3) Six is divisible by 3, and 10 is a multiple of 2.

True. 6/3 = 2 and 2 x 5 = 10. Both the conditions are true so it is also true.

4) The average of the data is greater than the largest value in the data, or it’s less than the largest value in the data.

True.

We have two conditions in this statement and an 'or' between them. One of the conditions is true that is "average is less than the largest value in the data". So the statement as a whole is true.

5) The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.

True.

6) If an equilateral triangle has equal angles, then all its angles will measure 45°.

False.

A triangle has 3 angles whose sum = 180 degrees.

For equilateral triangle each angle will measure 180/3= 60 degrees.

Answer:  2 following statements are true

The first true statement:

Six is divisible by 3, and 10 is a multiple of 2.

We know this because 6 is divisible by 3, and again proven by when we  divide 10 by 5 we get 2, so 10 is a multiple of 2.

The second true statement:

The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.

Step-by-step explanation:

Answer:

The number is 25

Step-by-step explanation:

we have

[tex]x^{2} -10x=7[/tex]

we know that

[tex]10/2=5[/tex]

so

Adds [tex]5^{2}[/tex] both sides

[tex]x^{2} -10x+5^{2}=7+5^{2}[/tex]

[tex]x^{2} -10x+25=7+25[/tex]

[tex]x^{2} -10x+25=32[/tex]

Rewrite as perfect squares

[tex](x-5)^{2}=32[/tex]

Answer:

m = -2

Step-by-step explanation:

This equation is in point-slope form

The numbers added or subtracted by a variable are a coordinate point.

y + 2 --> (0,-2)

x - 3 --> (3,0)

(3,-2)

The slope is represented by the number outside of the parentheses.

Therefore, the slope of the line is -2

Answer:

-2

Step-by-step explanation:

This equation is written in point slope form

y-y1 = m(x-x1)

where (x1,y1) is a point on the line and m is the slope

y- -2 = -2(x -3)

A point on the line is (-3, -2) and the slope is -2