Find an equation of the line with the slope m= - 8 that passes through the point (-3,-6). Write the equation in the form Ax +By = C.
Choose the correct answer below.
A. 8x +y = 30
B. 30x +y = - 8
C. 8x+y = - 30
D. 30x +y = 8

Answer:

B) μD = 0.60 ± 0.10(1.397)

Step-by-step explanation:

The confidence interval is given by:

[tex]MD±t_{\alpha/2, n-1} \frac{s}{\sqrt{n} }[/tex]

Where

MD=60

n=9

df=n-1=8

[tex]t_{\alpha/2, n-1}=1.397[/tex]

[tex]s=\sqrt{0.09} =0.3[/tex]

Then the confidence interval is

μD=0.60±1.397*(0.3/√9)

μD=0.60±0.10*(1.397)

The probability of choosing a Disney character that is not a mouse is 0.9 or 90%.

there are a total of 100 Disney characters, including Mickey Mouse, Minnie Mouse, and other mouse characters, summing up to 10 mice characters.

Therefore, the number of non-mouse characters is 100 - 10 = 90.

Total number of characters (N): 100

Number of mouse characters (M): 10

Number of non-mouse characters: N - M = 100 - 10 = 90

Probability of choosing a non-mouse character: (N - M) / N = 90 / 100 = 0.9

Thus, the probability that the randomly chosen Disney character is not a mouse is 0.9 or 90%.

The complete question is "Given that a Disney character is chosen at random, what is the probability that the character is not a mouse? If there are 100 Disney charater out of which 10 are mice chracter "

Quadratic functions and linear absolute value functions can be both increasing and decreasing within the same function. Linear, constant and exponential functions do not exhibit this behaviour.

In mathematics, a function can be both increasing and decreasing at different parts of its graph. This means that the function's value increases for some parts of the domain (the x-values) and decreases for others. Not every function type can show this behavior. Let's consider the options:

Therefore, the function types that can be both increasing and decreasing within the same function are quadratic functions and linear absolute value functions.

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Answer:

x = -9

y = 35/7

Step-by-step explanation:

Given equations :-

-7y - 4x = 1 ....... ( i )

7y - 2x = 53 ........ ( ii )

From ( i )

-7y = 1 + 4x

[tex]y = \frac{ - (1 + 4x)}{7} [/tex]

..........( iii )

From ( ii )

7y - 2x = 53

7y = 53 + 2x

[tex]y = \frac{53 + 2x}{7} [/tex]

.......( iv )

Equating both ( iii ) & ( iv )

y = y

[tex] \frac{ - (1 + 4x)}{7} = \frac{53 + 2x}{7} [/tex]

-(1 + 4x ) = 53 + 2x

-1 -4x = 53 + 2x

-1 - 53 = 2x + 4x

-54 = 6x

-54/6 = x

-9 = x

Also,

[tex]y = \frac{ - (1 + 4x)}{7 } \\ \\ y = - \frac{(1 + 4( - 9))}{7} [/tex]

[tex]y = - \frac{ (1 - 36)}{7} \\ \\ y = - \frac{( - 35)}{7} \\ \\ y = \frac{35}{7} [/tex]

Answer:

11

Step-by-step explanation:

The degree of a polynomial is he highest of the degrees of its monomials (individual terms) with non-zero coefficients.

You are given the polynomial

[tex]5a^6bc^2+8d^5+7e^6f^2-10g^4h^7[/tex]

It consists of 4 terms:

The degrees are:

The greatest degree is 11.

Answer:

11

Step-by-step explanation:

I did the quiz

Answer:

his cost depends on how many staplers he gets and the input is how much each stapler cost and output is how much he has to spend

Step-by-step explanation:

Answer:

A. Number of staplers.

B. Input is number of staplers and output is total cost.

Step-by-step explanation:

Part A : Let he bought x staplers,

∵ The cost of each stapler = $ 16.99

So, the cost of x staplers in dollars ( say y ) = price of each staplers × number of staplers

⇒ y = 16.99x  

Which is the required equation that shows the given scenario,

∵ y ∝ x,

I.e. his final cost would depend upon the number of staplers.

Part B :

∵ in the equation y = 16.99x

x = input value, y = output value,

Thus, in this scenery, input is the number of staplers and output is total cost.

Yochanan walked 5 km to the bus stop at 5 km/h and then took the bus for the remaining 30 km at 60 km/h, totaling 1.5 hours for his trip to school.

The question involves calculating distances and times related to Yochanan's trip from home to school, requiring the application of speed, distance, and time relationships. Let's denote the distance from Yochanan's home to the bus stop as x kilometers and the remaining distance to school (35 - x) kilometers. Given the average speeds and the total trip time, we can set up equations to solve for x.

The time taken to walk to the bus stop is x / 5 hours, and the time taken to travel from the bus stop to school by bus is (35 - x) / 60 hours. The total trip time is 1.5 hours.

Therefore, the equation is:

x / 5 + (35 - x) / 60 = 1.5

Solving this equation:

So, Yochanan walked 5 km to the bus stop. Using the distance to calculate times, he spent 1 hour on the bus and 0.5 hours walking.

Answer:

Hello My Friend! The correct answer its double root.

Step-by-step explanation:

In this equation, if we applie the a, b and c coefficients (a=1, b=4, c=4) ind the Bhaskara, the final result will be 4 for both cases. x'=4 and x''=4. It happens because the number of theta is equal to 0. So, both roots will be the same number.

Answer:

The answer to your question is: it's a rectangle

perimeter = 30 u

Step-by-step explanation:

d = √((x2.x1)² + (y2-y1)²)

Now, calculate the distances AB, BC, CD, AD

dAB = √((11-6)² + (-4+4)² = √5² = 5

dBC = √((11-11)² + (-4-6)² =√10 = 10

dCD = √((6-11)² + (6-6)² = √5² = 5

dAD = √((6-6)² + (6+4)² = √10² = 10

From the results we conclude that is a rectangle because two sides have the same length and the other two also measure the same. We can draw it to confirm this.

Perimeter = dAB + dBC + dCD + dAD

                 = 5 + 10+ 5 + 10 = 30 units

To determine the shape of the quadrilateral, calculate the distances between the vertices and check for equal side lengths and 90-degree angles. The given quadrilateral is a parallelogram since the opposite sides are parallel and equal. The perimeter of the quadrilateral is 30 units.

To determine whether the given quadrilateral is a square, a rectangle, or a parallelogram, we can use the properties of each shape. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is a quadrilateral with opposite sides equal in length and all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To find the perimeter of the quadrilateral, we can calculate the sum of the lengths of all four sides.

Calculating the distances between each pair of given points:

The distances between the vertices are: AB = 5, BC = 10, CD = 5, and DA = 10. Therefore, the perimeter of the quadrilateral is 5 + 10 + 5 + 10 = 30 units.

Answer:

d. 69.8 mph

Step-by-step explanation:

Since, the ratio of the diameter of the tyre of a vehicle and its speed must be constant,

Given,

The original diameter of the tyre = 29 inch,

Original speed = 60 mph,

Thus, the ratio of diameter and the speed of the vehicle = [tex]\frac{29}{60}[/tex]

New diameter of the tyre = 33.73 inch,

Let x be the new speed of the vehicle = [tex]\frac{33.73}{x}[/tex]

[tex]\implies \frac{29}{60}=\frac{33.73}{x}[/tex]

[tex]\implies x=\frac{33.73\times 60}{29}=69.79\approx 69.8\text{ mph}[/tex]

Hence, the actual speed of the vehicle would be 69.8 mph.

OPTION D is correct.

Answer:

5x-2y=-4

Step-by-step explanation:

2x-5y=0

eq. of line perpendicular to ax+by=c is bx-ay=d,d is calculated by the given condition.

line perpendicular to 2x-5y=0 is 5x+2y=c

if it passes through (-2,3) ,then

5*-2+2*3=c

c=-10+6=-4

reqd. eq. is 5x+2y=-4

The final marble left in the bag will be red.

Let, analyze the process step by step:

Initially, the bag contains 99 red marbles and 99 blue marbles.

When you take two marbles out of the bag, there are two possibilities: either you get two red marbles or two blue marbles, or you get one red and one blue marble.

a. If you get two marbles of the same color (both red or both blue), you put a red marble in the bag.

b. If you get one red and one blue marble, you put a blue marble in the bag.

After putting a marble back in the bag, you have one less marble in the bag.

You repeat this process, reducing the number of marbles in the bag by one each time, until only one marble is left in the bag.

Now, let's think about the outcomes at each step:

If the bag contains an odd number of marbles (99 red + 99 blue = 198), the final marble will be red because at each step, you are adding a red marble back to the bag.

If the bag contains an even number of marbles (e.g., 100 red + 100 blue = 200), the final marble will be blue because at each step, you are adding a blue marble back to the bag.

In this case, the bag contains 99 red marbles and 99 blue marbles, which is an odd number (198 marbles).

Therefore, the final marble left in the bag will be red.

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Answer:

There are 1752574320 outcomes

Step-by-step explanation:

The option are:

1      11      21      31      41      51      61      71      81      91

2     12     .         .         .         .        .         .        .         .    

3     13     .         .         .         .        .         .        .         .

4     14     .         .         .         .        .         .        .         .

5     15     .         .         .         .        .         .        .         .

6     16     .         .         .         .        .         .        .         .

7     17     .         .          .         .        .         .        .         .

8     18     .         .          .         .        .        .         .         .

9     19     .         .          .         .        .        .         .         .

10    20    .         .          .         .        .        .         .         .

So we have to select 5 numbers, with  the property that the last digits of all five numbers are different

__ __ __ __ __

1. Have 90 options

⇒ 90

2. Have 90 - 9 options (e.g. if 2 was the first chosen number, then you can't select more 2, 12, 22, 32, 42, 52, 62, 72 or 82 )

⇒ 90 - 9 = 81

3. Have 90 - 9 that can't no be chosen more because share the same last number as the first number - 9 that can't no be chosen more because share the same last number as the second number

⇒ 90 - 9 - 9 = 72

4. Have 90 - 9 that can't no be chosen more because share the same last number as the first number - 9 that can't no be chosen more because share the same last number as the second number - 9 that can't no be chosen more because share the same last number as the third number

⇒ 90 - 9 - 9 - 9 = 63

5. Have 90 - 9 that can't no be chosen more because share the same last number as the first number - 9 that can't no be chosen more because share the same last number as the second number - 9 that can't no be chosen more because share the same last number as the third number - 9 that can't no be chosen more because share the same last number as the fourth number

⇒ 90 - 9 - 9 - 9 - 9 = 54

So now the number of possible combination with the given restriction is equal to the multiplication of the amount of option for the selection of each number (90 for the selection of the first, 81 for the selection of the second, 72 for the selection of the third number, 63 for the selection of the fourth and 54 for the selection of the fifth)

C= 90*81*72*63*54 = 1752574320

There are 1752574320 outcomes

Final answer:

There are 30,240 outcomes with the property that the last digits of all five numbers are different.

Explanation:

To calculate the number of outcomes with the property that the last digits of all five numbers are different, we need to consider each digit separately. For the first number, we have 10 choices (0-9), for the second number, we have 9 choices (since the last digit of the first number is taken), for the third number, we have 8 choices, and so on.

Therefore, the total number of outcomes is:

10 x 9 x 8 x 7 x 6 = 30,240.

Final answer:

The probability that no employee in the sample work at the plant in Hawaii is 0.0279, the probability that one of the employees in the sample works at the plant in Hawaii is 0.2656, the probability that two or more of the employees in the sample work at the plant in Hawaii is 0.7065, and probability that nine of the employees in the sample work at the plant in Texas is 0.06.

Explanation:

To find the probability that none of the employees in the sample work at the plant in Hawaii, we need to find the probability of selecting 0 employees from the Hawaii plant out of a total sample size of 10 employees. Since there are 20 employees at the Hawaii plant and 60 employees in total, the probability is:

P(selecting 0 employees from Hawaii) = (20C0 * 40C10) / (60C10) = 0.0279

To find the probability that one of the employees in the sample works at the plant in Hawaii, we need to find the probability of selecting 1 employee from the Hawaii plant out of a total sample size of 10 employees. The probability is:

P(selecting 1 employee from Hawaii) = (20C1 * 40C9) / (60C10) = 0.2656

To find the probability that two or more of the employees in the sample work at the plant in Hawaii, we need to find the probability of selecting 2 or more employees from the Hawaii plant out of a total sample size of 10 employees. The probability is:

P(selecting 2 or more employees from Hawaii) = 1 - P(selecting 0 employees from Hawaii) - P(selecting 1 employee from Hawaii) = 1 - 0.0279 - 0.2656 = 0.7065

To find the probability that nine of the employees in the sample work at the plant in Texas, we need to find the probability of selecting 9 employees from the Texas plant out of a total sample size of 10 employees. The probability is:

P(selecting 9 employees from Texas) = (40C9 * 20C1) / (60C10) = 0.06

Answer:

56 chairs

Step-by-step explanation:

856+700=1556    <--- expected count

chairs set up= 1500

1556-1500= 56 more chairs

Answer: A.)  56 more

Step-by-step explanation:

Answer:64.389

Step-by-step explanationthe new volume in each cylinder will be the volume of water + volume 1 cube (assuming the cubes does not float on water)

then volume of a cube =side^3=(2.90 cm)^3= 24.389cm^3=24.389mL

(considering that 1 ml= 1 cm^3)

Finally the new level of each cylinder is=40 mL+24.389mL=64.389 mL

(if the cube float we need to consider the volume under water (with densities which are not given)

Answer: [tex](0.0228\ ,0.0706)[/tex]

Step-by-step explanation:

Given : Sample size : n= 300

The sample proportion of defectives : [tex]\hat{p}=\dfrac{14}{300}=0.0467[/tex]

Significance level for 95% confidence level =[tex]\alpha=1-0.95=0.05[/tex]

Critical z-value:[tex]z_{\alpha/2}=\pm1.96[/tex]

Confidence interval for population proportion :

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]= 0.0467\pm (1.96)\sqrt{\dfrac{0.0467(1-0.0467)}{300}}[/tex]

[tex]\approx\ 0.0467\pm 0.0239\\\\=(0.0467-0.0239\ , \ 0.0467-0.0239)\\\\=(0.0228\ ,0.0706)[/tex]

Hence, a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool= [tex](0.0228\ ,0.0706)[/tex]

Answer:

[tex]39\ parking\ attendants[/tex]

Step-by-step explanation:

Let

x -----> the number of blue lots

y-----> the number of red lots

we know that

[tex]x+y=15[/tex] ------> equation A

we have that

[tex]x=0.60(15)=9\ blue\ lots[/tex]

[tex]y=0.40(15)=6\ red\ lots[/tex]

The total parking attendants required for tonight's event is equal to the product of the number of blue lots by three plus the product of the number of red lots by two

so

[tex]9(3)+6(2)=39\ parking\ attendants[/tex]

Answer:

39

Step-by-step explanation:

Answer:

For the first question, 180 degrees equals to a half of the sphere. For the second question, you need 24 central meridians for a complete sphere, which are exactly the hours in a day.

Step-by-step explanation:

A sphere is basically a 3D circle. As a circle has 360 degrees, 180 degrees would be half of a circle. Imagine you are on a satellite over the north pole or the south pole and you have a way to cut the earth by the middle. You will get two halves of sphere.

About the second question, you may need to have in mind that a day is the time spent for the earth to rotate all 360 degrees over its own axis. British fellow, on XIX century, decided they were the center of the world. As previously, back in the days, some other people decided a day had 24 hours, they decided to draw this lines and divide the earth in 24 pieces, so they could knew which time was on every point their extense kingdom had.  As I said, a circle has 360 degrees, (360 degrees)/(24 hours) equals to 15 degrees.

Answer:

not 55

Step-by-step explanation:

Answer:

220

Step-by-step explanation:

Answer:

C. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.

Step-by-step explanation:

We draw the vector u=A at the origin of a Cartesian plane. then at the same point, we draw -v = -B. To find the vector that represents u-v = A-B, straight lines are drawn parallel to each vector, forming a parallelogram. The resulting vector will be the diagonal of the parallelogram that begins at the origin of the plane.

Answer: So you have n students, where n>13, and m classrooms, where 3>m>13.

the question asked is: is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

The only situation where it will be possible is when you take the total number of students, divide it by the number of classrooms and the result is a whole number ( because here we are working with students, you can't have a 2/5 of a student, for example)

So n/m must be a natural number.

So now suppose that n is prime, this is : n only can be divided by itself, an example of a prime number is 17.

so if you have n = 17 students, there is no m that divides 17 into a whole number, then in this case, you can't assign the same number of students to each classroom.

And because we find a counterexample, so it is not possible for every n and m, so the statement is false. ( independent of the fact that you actually could do this for some m and n given, the important thing here is that you can't do it for every combination of m and n)

Answer:

$185,000

Step-by-step explanation:

We have been been given that during the​ year, Fast Dry Corporation has $ 340,000 in​ revenues, $ 155,000 in​ expenses, and $ 12,000 in dividend declarations and payments.

We will use following formula to solve our given problem.

[tex]\text{Net income}=\text{Revenues}-\text{Expenses}[/tex]

[tex]\text{Net income}=\$340,000-\$155,000[/tex]

[tex]\text{Net income}=\$185,000[/tex]

Therefore, the net income for the year was $185,000.

Answer:

The correct answer is 90

Step-by-step explanation:

Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).

We need to find a, h and k.

The focus is half way between the vertex and directrix.

You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).

From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.

We have all that is needed to form our equation.

(x - (-3))^2 = 4(2)(y - 0)

(x + 3)^2 = 8y

Done.

Answer:

i think this will help (x - (-3))^2 = 4(2)(y - 0)

(x + 3)^2 = 8y

Step-by-step explanation:

Answer:

option (c) 475

Step-by-step explanation:

let the automobile installment credit be 'C'

Given:.

Automobile installment credit accounted for 36 percent of all outstanding consumer installment credit

Now,

57 billion is [tex]\frac{1}{3}[/tex] of automobile installment credit

or

57 billion = [tex]\frac{1}{3}[/tex] × C

or

C = 57 × 3

or

C = 171 billion

now,

installment credit accounted = 36% of all outstanding consumer installment credit

or

171 billion = 0.36 × all outstanding consumer installment credit

or

All outstanding consumer installment credit = $475 billion

Hence, the correct answer is option (c) 475

Answer:

[tex]f(x)=6x+9[/tex]

Step-by-step explanation:

Functions have independet variables(the value of the variable could be any number, we have no restrictions) and dependent variaariables(the values of this variables depends of idependent variables)

the problem says that x is the independent variable, so we say that y is a dependent variable. Dependent need to be replaced by funcion notation, in this case we use y=f(x)

So we raplace it in the equation and we have:

[tex]f(x)-6x-9=0[/tex]

we solve for f(x) passing -6x and -9 to the right side and changing the signs, and we get:

[tex]f(x)=6x+9[/tex]

Answer:

f(x) = 6x + 9

Step-by-step explanation:

The question is not complete because the are no option to pick from. This is the complete question.

Consider the function represented by the equation y minus 6 x minus 9 = 0. Which answer shows the equation written in function notation with x as the independent variable?

f of x = 6 x + 9

f of x = one-sixth x + three-halves

f of y = 6 y + 9

f of y = one-sixth y + three-halves

writing this in as a function

[tex]f(x)-6x-9=0[/tex]

the question is asking us to write the function in such a way that x is the independent variable

[tex]f(x)=6x-9[/tex]

here x is the dependent variable

to make x independent, we need to solve for x

[tex]-9=6x\\[/tex]

divide both sides by 6 to make x independent

[tex]\frac{-9}{6} =x\\\\\\\x=\frac{-3}{2}[/tex]

Answer:

x = 22

Step-by-step explanation:

Adding all the degrees to a triangle must equal 180

120 + (x+16) + x = 180

2x + 136 = 180

     -136.   -136

2x = 44

[tex]\frac{2x}{2}  = \frac{44}{2}[/tex]

x = 22

Final answer:

To find the value of x in the triangle with given angles, apply the rule that the sum of a triangle's interior angles is 180 degrees.

Explanation:

The value of x can be found by using the fact that the sum of the interior angles of a triangle is 180 degrees.

Angles of the triangle are given as 120 degrees, (x + 16) degrees, and x degrees.

Setting up the equation: 120 + (x + 16) + x = 180 and solving for x gives x = 22 degrees.