Which of the following is equal to 7.5 × 4? A. (7 × 4) + (0.5 × 7) B. (7 × 4) + (0.5 × 4) C. (7 + 4) × (0.5 + 4) D. (7 × 4) × (0.5 × 4)

Answer:

up is equal to 5/ 6

left side is equal to 3/4

Step-by-step explanation:

1/6 + 1/6+ 1/6+ 1/6+ 1/6= 5/6

1/4 + 1/4 + 1/4= 3/4

Answer:

rational numbers and irrational numbers

Step-by-step explanation:

Here are the expressions on the left matched with the simplifed form on the right:

Here are some mathematical rules:

Also, this sign | | indicates that the number is postive.

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Answer:

Coordinate A ins not intercepting any axis.

Step-by-step explanation:

For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]

Since in (3, 6), none of the components are 0, it is not intercepting any axes.

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center,  (-3, 2 , 5) and radius 4 becomes

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]

Then,

[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]

Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes

[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]

This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]

This is the part of the sphere that intersects with the yz-plane.

Answer:

Step-by-step explanation:

Product—Multiplication

Sum— Addition

Difference—Subtraction

Quotient—Division

Quantity— Parenthesis

Answer:

y = 2/7x + 7

Step-by-step explanation:

We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other.  So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.

Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.

5 = -14/7 + b

5 = -2 + b

7 = b

Finally, plug the b value into your final equation and you will have your answer.

the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.

Question:

Express each vector as a product of its length and direction.

[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

Answer:

[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

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

Let the given vector be v, i.e

[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

(i) The length/magnitude |v| of vector v is therefore,

|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]

|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]

|v| = [tex]\sqrt{(\frac{3}{6})[/tex]

|v| = [tex]\sqrt{(\frac{1}{2})[/tex]

|v| = [tex]\frac{1}{\sqrt{2}}[/tex]

(ii) The unit vector u in the direction of vector v, is therefore,

u = [tex]\frac{v}{|v|}[/tex]

[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]

[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Answer:

He did not check for extraneous solutions.

Step-by-step explanation:

He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.

Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.

Answer: He did not check for extraneous solutions.

Answer:

7

Step-by-step explanation:

Answer:

A) sin 70 = x/10

Step-by-step explanation:

From the angle 70 degrees, 10 is the hypotenuse and x is the opposite and if we go by SOH-CAH-TOA I have an O and a H so its sin.

so we know it's sin so we need to figure out the equation. since we have a hypotenuse as a factor it is on top. and the other number is on the bottom.

so,

A) sin 70 = x/10

Answer: C. The bakery should conduct an observational study

Step-by-step explanation:

From the question, we are informed that a bakery wants to determine the best placement for day-old goods. The type of data collection source that the bakery should use is an observational study.

An observational study is a form of study whereby the individuals who are to be observed are being studied by the researcher and certain conclusions are derived about them. When the bakery conductd an observational study, the behavior of the customers regarding goods placement can be observed.

Answer:

for the first question at the top, x=10

Step-by-step explanation:

x+3+9x=8x+23

(subtract 8x from both sides)

x+3+x=23

(combine the x terms)

2x+3=23

(subtract 3 from both sides)

2x=20

(divide by 2 from each side)

x=10

Answer:

1. RATIO SCALE

2. INTERVAL SCALE

3. NOMINAL SCALE

4. ORDINAL SCALE

Step-by-step explanation:

The scales are:

- Nominal Scale

- Ordinal Scale

- Interval Scale

- Ratio Scale

Rule: Each scale will be used exactly once.

For number 1, the description is that of a Ratio Scale because size comparisons can be made between values on the scale, such as the example given - that one value is twice as big as another value.

For number 2, the description is that of an Interval Scale because the values of data measured on the scale can be ranked e.g. Yes ranks as 1, No ranks as 2, Indifferent ranks as 3 and there is meaningful difference (not numerical difference) between scale points.

For number 3, the description is that of a Nominal Scale, because it says obviously that the values of data measured on this scale can be in form of names (watch out for keywords like this when reading through) and cannot be rank ordered! A good example is the following data set:

- Yellow, Brown, Purple, Cream, Fustian Pink

For number 4, the description is that of an Ordinal Scale. A keyword "rank" is to be given attention here, even as the statement is straightforward and gives just a simple information.

Answer:

(2)

Step-by-step explanation:

Answer:

$818,3

Step-by-step explanation:

16.7% in decimal is 0.167

= 0.167 x $4900

= $818,3

Answer:

-4d

Step-by-step explanation:

Answer:

6Y

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

[tex]R=3\times 2\times Y[/tex]

We know that, 3×2 = 6

So,

[tex]R=6Y[/tex]

Hence, Thrice the product of two and "Y" is 6Y.

Answer:

9

Step-by-step explanation:

-4.5 x (-2) is equal to 9

Answer:

b = 12

Step-by-step explanation:

15 - 2b = -9

Minus 15 to both sides

-2b = -24

Divide both sides by -2

b = 12

Given :

Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .

To Find :

The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .  

Solution :

Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :

[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]

Now , mid point is given by :

[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]

Hence , this is the required solution .

Answer:

The value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Step-by-step explanation:

We are given that C is the midpoint of segment AB where A(-3,m) , B (4, -1) , and C (k, 2).

As we know that the mid-point formula states that;

Mid-point = [tex]\frac{a+b}{2}[/tex]

This means that;

Mid-point of AB = [tex]\frac{A+B}{2}[/tex]

C(k, 2) = [tex](\frac{-3+4}{2}, \frac{m+(-1)}{2} )[/tex]

C(k, 2) = [tex](\frac{1}{2}, \frac{m-1}{2} )[/tex]

This means that;

[tex]k = \frac{1}{2}[/tex]  and  [tex]2=\frac{m-1}{2}[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m-1=4[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m = 4+1 = 5[/tex]

So, the value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Answer:

-15

Step-by-step explanation:

-10+-9=-19+4=-15

Answer:

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]

Step-by-step explanation:

We need to evaluate the following integral by interpreting it in terms of areas :

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]

The first step is to separate the integral into two easier integrals

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex]    (Integral of the sum)

Now we can calculate each integral by studying the area below each function.

For the first integral the function is [tex]f(x)=1[/tex]

(I will attach a file with the functions)

The area below this function is the area of a rectangle with sides 1 and 3 ⇒

[tex]\int\limits^0_{-3}1 \, dx=3[/tex]

For the second integral the function is

[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]

If we study this function :

[tex]y=\sqrt{9-x^{2}}[/tex]

[tex]y^{2}=9-x^{2}[/tex] (I)

[tex]x^{2}+y^{2}=9[/tex]

Which is the equation of a circle centered at (0,0) with radius equal to 3

From the equation (I)

[tex]y^{2}=9-x^{2}[/tex]

[tex]|y|=\sqrt{9-x^{2} }[/tex]

The two possible solutions are :

[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]

We will use (II) to solve the integral (which is the upper part of the circle)

The area of a circle with radius equal to 3 is

[tex]\pi.3^{2}[/tex]

In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]

Finally the integral is equal to

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]

Answer:

Negative infinity

Step-by-step explanation:

The line points down infinitely in the graph.

Answer:

-17 × 0 = 0

every number multiplied by 0 is equal to 0

Answer:

24

Step-by-step explanation:

[tex]a^{2}[/tex]= 49 because any number squared is positive.

Since b=2,

2(-4)= -8.

Then this is 49-8-17, which equals 24.

Answer:

24

Step-by-step explanation:

Answer:

Step-by-step explanation:

12.3 + 9.6 = 21.9

The expression 12.3 - (-9.6) is equivalent to 21.9.

Given is an expression 12.3 -(-9.6) = 12.3 + 9.6, we need to simplify it,

To simplify the expression 12.3 - (-9.6), we can rewrite it as 12.3 + 9.6.

When subtracting a negative number, it is equivalent to adding the positive value of that number.

So, -(-9.6) becomes +9.6.

Therefore, 12.3 - (-9.6) simplifies to 12.3 + 9.6.

Adding 12.3 and 9.6 gives us 21.9.

So, 12.3 - (-9.6) = 21.9.

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Answer:

10 x 10 x 10 x 10.

Step-by-step explanation:

2(5)^4

10^4

Expanded form; 10*10*10*10.

Answer:

10 x 10 x 10 x 10

Step-by-step explanation: