Mathematics College

(I will give Brainliest/5 stars to correct answer)
Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

A) <28, -12>
B) 16
C) -40
D) <11, -1>

Answers

Answer 1
a•b = 7*4 +(-4)*3
= 28 -12
= 16 . . . . . matches selection B
Answer 2
To find the dot product you multiply the corresponding coordinates and then add up the products

a dot b = dot product between the vectors 'a' and 'b'
a dot b = 7*4 + (-4)*3
a dot b = 28 - 12
a dot b = 16

Answer: Choice B) 16

Related Questions

A city council consists of six democrats and five republicans. If a committee of seven people is selected, find the probability of selecting four Democrats and three republicans.

Answers

Use hypergeometric distribution where there are two categories of identical objects/persons, each with a know size.
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then 
[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
where 
[tex]C(n,r)=\frac{n!}{(n!(n-r)!)}[/tex]  = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7

[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
[tex]P(4,3)=\frac{C(6,4)C(5,3)}{C(6+5,4+3)}[/tex]
[tex]=\frac{C(6,4)C(5,3)}{C(11,7)}[/tex]
[tex]=\frac{15*10}{330}[/tex]
[tex]=\frac{5}{11}[/tex]

Answer: the probability of selecting 4 Democrats and 3 Republicans is 5/11

Suppose that g(x) = f(x – 8). Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 8 units to the left.
B. The graph of g(x) is the graph of f(x) shifted 8 units down.
C. The graph of g(x) is the graph of f(x) shifted 8 units up.
D. The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Answers

D. The graph of g(x) is the graph of f(x) shifted 8 units to the right.

The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

What is shifting of a function?

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

According to the question

g(x) = f(x – 8)

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

Hence, The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

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Can you please help me out ?

Answers

What you can do for this case is to use the following trigonometric definition.
 sine (x) = a / h
 Where,
 a: side of the triangle.
 h: hypotenuse.
 Substituting:
 sine (x) = 3/6
 x = Arcosine (1/2)
 x = 30 degrees.
 The other angle is:
 180-30-90 = 60 degrees
 Answer:
 W = 30
 V = 60
 U = 90
 option 4

Solve using the arrow way
430-230?

Answers

To substract the numbers shown by the method known as the "Arrow way" you must rewrite 430 and substract the hundredths (In this case, it is 200). Then you have to substract the tenths to that result (Result obtained-30). This explanation is shown below:

 430 --( -200 )---> 230 --( -30 )---> 200

 Therefore, the solution of the mathematical operation 430-230, using the arrow way, is: 200 

Jose and Sue are playing a board game. If they land on a red or blue square, they lose 1 point. The inequality statement compares the magnitude of their scores at the end of the game. |−2|<|−5| What does the inequality statement show?

Answers

Final answer:

The inequality statement |−2|<|−5| shows that 2 is less than 5.

Explanation:

In mathematics, an inequality compares two expressions or values, indicating their relative size. Symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) represent inequalities.

The inequality statement |−2|<|−5| compares the magnitude of two numbers, -2 and -5. To find the absolute value of a number, we remove the negative sign. So, |−2| is equal to 2 and |−5| is equal to 5. Therefore, the inequality statement |−2|<|−5| means that 2 is less than 5.

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Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?

Answers

11 + 4(x + 2y + 4)
= 11 + 4x + 8y + 16 ..........distributive property
= 4x + 8y + 27  .................combine like terms

There is an ice cream and candy shop next-door that is the same size as your bakery. How many 30th of the space does it take up

Answers

Well, this is basically perimeter and Area. So, if there next door, your going to want to find out 50% of the ice cream shop and candy shop. 40% of it is next to each other . So 40 x 2= 80, there’s the answer . Hope this helps!!!

you lease a car valued at 23,495 for 3 years at $429.95/month with a $500 down payment. If interest is 30% of the payment, how much interest is paid over the 3 years?

Answers

(36 payments)*($429.95)*30% = $4,643.46 . . . . interest paid over 3 years

Solution:

Present Value of car= $ 23,495

Down Payment = $ 500

Total Amount paid monthly for 3 years that is 36 months, if you pay $ 429.95 per month=$ 15478.20

Total amount paid for the car as an agreement which includes Down payment of $ 500 as well as monthly Payment of $ 429.95 for 36 months= $ 15478.20+$ 500=$ 15978.20

As, given Interest is  30% of the payment.

So, total interest = 30% of $ 15978

[tex]=\frac{30}{100}\times 15978.20[/tex]

= $ 4793.40

But if you will calculate interest on payment of $ 429.95 at the rate of 30%, it gives

[tex]=\frac{30}{100}\times 429.95[/tex]

= $128.985

So, total interest for 3 years= $128.985 ×36=$ 4643.46

Also, if you will calculate interest on payment of ($500+$429.95=$929.95) at the rate of 30%

[tex]=\frac{30}{100}\times 929.95[/tex]

=$278.985

Total interest for 3 years= $278.985 ×36=$10,043.46

Alex lives eight tenth of a mile from Sarah. What is eight tenths written as a decimal

Answers

Hello!

Eight tenths = 8/10

To convert a fraction to a decimal, we must divide the numerator by the denominator.

8 ÷ 10 = 0.8

Eight tenths is 0.8 as a decimal.
the answer is 0.8 

I hope this helps

What does the random variable for a binomial experiment of n trials measure?the random variable measures the number of successes out of n trials.the random variable measures the number of failures out of n trials. the random variable measures the standard deviation of n trials.the random variable measures the mean of n trials?

Answers

My answer is the random variable measures the number of successes out of n trials.

A binomial random variable is defined as the number of successes x in n repeated trials of a binomial experiment. It is more feasible to measure the number of successes than the number of failures because the more successes you have, the nearer you are to your desired goal in a binomial experiment. 

Answer:

The random variable measures the number of successes out of n trials.

How many possible outcomes are there from choosing an outfit from a blue shirt, a red shirt, black shorts, tan shorts, a pair of sneakers, and a pair of sandals?

Answers

2 shirts
 2 shorts
2 shoes

2 x 2 x 2 = 8 different ways

What fraction of the circle does the shaded angle represent??

Answers

The fraction of the circle that is not shaded is 3/4 
The fraction of the circle that is shaded is 1/4 
shaded part is 1/4

non shaded ( not shaded) is 3/4

altogether it would be 4/4 or one whole

which of the following functions gives the length of the base edge

Answers

The answer is b hope is the correct one
Answer:
a = sqrt(3v/8) which is the first choice

Explanation:
The volume of the right square pyramid is calculated using the following rule:
V = (1/3)*h*a^2 where:
V is the volume
a is the length of the base
h is the height
We are given that the height = 8 in and volume = v, this means that:
v = (1/3)*8*a^2 = (8/3)*a^2

Now, we will solve this equation for a as follows:
v = (8/3)*a^2
3v = 8a^2
3v/8 = a^2
a = sqrt(3v/8) which is the first choice

Hope this helps :)

HELP SUPER FAST PLS A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?

Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches

Answers

ok, so area/width=length

then they gave you mixed fractions
they want you to practice converting mixed fractions into improper fractions and dividing them

rmember, improper fractions are a/b where a>b sometimes

and also remember that [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex]


okie dokie

width
4 and 1/2=width
4+1/2=width
8/2+1/2=width
9/2=width


area=36 and 3/4
area=36+3/4
area=144/4+3/4
area=147/4

so area/width=length
[tex]\frac{\frac{147}{4}}{\frac{9}{2}}=length[/tex]
[tex]\frac{(147)(2)}{(4)(9)}=length[/tex]
[tex]\frac{294}{36}=length[/tex]
[tex]\frac{49}{6}=length[/tex]
[tex]\frac{48}{6}+\frac{1}{6}=length[/tex]
[tex]8+\frac{1}{6}=length[/tex]

so the length is [tex] 8 \space\ and \space\ \frac{1}{6} \space\ in[/tex]

Answer:

8 1/6

Step-by-step explanation:

hope it helps

How many quarter inches long is 7 3/4

Answers

The number of quarters in 7 is 28 and the number of quarters in 3/4 is 3. Then the total number of quarters is 33.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The quarter is written as one-fourth.

[tex]\rm quarter = \dfrac{1}{4}[/tex]

We have 7 + 3/4

We know that one has 4 quarters then 7 has

→ 7 × 4 = 28

And 3/4 has three quarters.

Then the total quarter will be

[tex]\rm Number\ of \ quarter = 7 \dfrac{3}{4} \times 4 = \dfrac{33}{4} \times 4 = 33[/tex]

More about the fraction number link is given below.

https://brainly.com/question/78672

Final answer:

There are 31 quarter inches in 7 3/4 inches. This is determined by converting the mixed number into an improper fraction and then dividing by ¼, which gives us 31/4 or 31 quarter inches.

Explanation:

The question asks how many quarter inches there are in 7 3/4 inches. To find this, we can convert the mixed number into an improper fraction and then divide by the fraction representing a quarter inch (¼ inch).

First, convert 7 ¾ to an improper fraction by multiplying the whole number 7 by the denominator 4 and then adding the numerator 3. This gives us 28 + 3 = 31, so 7 ¾ inches is equivalent to ⅔31/4 or 31 quarter inches. Therefore, 7 3/4 inches is 31 quarter inches long.

which is more, 5,998 millimeters or 6 meters

Answers

6 meters of course is the answer

A protractor is used to measure an angle. Which of the following could be the measure of the angle if we know it is an acute angle?
125°
75°
0°
it can't be determined

Answers

Final answer:

To find an acute angle using a protractor, choose the angle less than 90°. The acute angle could be 75°.

Explanation:

To determine an acute angle using a protractor, we look for an angle that is less than 90 degrees, as acute angles are those that measure less than 90 degrees.

75° could be the measure of the angle as it falls within the range of acute angles.

Hence, in this case, the angle that could be the measure of the acute angle is 75°.

Please help me with questions 8 and 9

Answers

Problem 8

Answer: Choice A
Coordinates have been multiplied by a scale factor of 0.5

For instance
A = (-3, 4)
Multiply the coordinates by 0.5 to get
-3*0.5 = -1.5
4*0.5 = 2
So the coordinates of A' are (-1.5, 2) which is what matches what we're given above. The same will happen with B and C as well. 

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

Problem 9

Answer: choice C) x = 25; larger angle is 107 degrees

Work Shown:
(3x+32)+(x+48) = 180
4x+80 = 180
4x = 100
x = 25
If x = 25, then,
3x+32 = 3*25+32 = 107
x+48 = 25+48 = 73
So the larger angle is 107

Select the ratios that are equivalent to 3 boys and 5 girls

Answers

You have given no choices, but here are some.
6/10
9/15
12/20
15/25

Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 14 that height. Which of these statements is NOT true?

Answers

the correct question is 
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 that height. Which of these statements is NOT true?

the statements  in the attached figure

we know that 
r=2 cm
h1=8 cm
h2=(1/4)*8=2 cm
[Volume of cone 1]=(π*r²*h)/3--------> (π*2²*8)/3= 33.49 cm³
[Volume of cone 2]=(π*r²*h)/3--------> (π*2²*2)/3---------> 8π/3= 8.37 cm³

Statements A)
The volume of the smaller cone is (1/4)(1/3π • 2 • 2 • 8) cm3---------> is  true

Statements B)
The volume of the smaller cone is (1/3)(4π • 2) cm3.-----------> is  true

Statements C)
The volume of the smaller cone is (8/3)π cm3. -----------> is  true

Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

the answer is the Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

A graphic designer is planning the layout for a magazine advertisement of three pictures, shown below. The ratio of the sum of the widths of the three pictures to the total width of the advertisement is 4:5. If each picture is 4 inches wide, what is the length of each of the four empty spaces between the pictures (t)?

Answers

The length of each space is 3/4 in.

Let S be the sum of the width of the pictures and T be the total width of the advertisement.  Our proportion would be
[tex]\frac{S}{T}=\frac{4}{5}[/tex]

Since there are 3 pictures and each is 4 inches long, S=3*4=12:
[tex]\frac{12}{T}=\frac{4}{5}[/tex]
Cross multiplying, we have:
12*5=4*T
60=4T
Divide both sides by 4:
60/4 = 4T/4
15=T
The total width of the advertisement is 15 inches.  Subtract the known width of the pictures from this, 12, and we have 3 inches left over for the total of the 4 spaces.  Thus our answer is 3/4.

One positive integer is 6 less than twice another. The sum of their squares is 468. Find the integer

Answers

I think I deserve your points and brainliest :^)

The two integers are 12 and 18.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, one positive integer is 6 less than twice another.

Let positive integer be x and the other positive integer is 2x-6

x²+(2x-6)²=468

x²+4x²-24x+36=468

5x²-24x+36-468=0

5x²-60x+36x-432=0

5x(x-12)+36(x-12)=0

(x-12)(5x+36)=0

(x-12)=0

x=12

So, 2x-6=18

Therefore, the two integers are 12 and 18.

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James Callahan has available a 10% alcohol solution and a 60% alcohol solution. Find how many liters of each solution he should mix to make 50 liters of a 40% alcohol solution?

Answers

Let
x-------------> liters of 10% alcohol solution
y-------------> liters of 60% alcohol solution

we know that
x+y=50----------------------> x=50-y-----------------> equation 1
0.10x+0.60y=0.40*50----------> 0.10x+0.60y=20---------> equation 2

substitute 1 in 2 
0.10*(50-y)+0.60y=20---------> 5-0.10y+0.60y=20
5+0.50y=20------------> 0.50y=15-----------------> y=30
x+y=50----------> x=50-30---------> x=20

the answer is
20 liters of 10% alcohol solution
30 liters of 60% alcohol solution

PLZ HELP!! 20 points!

Is (3,-2) the solution to this system of equations? show how you determined your answer.

-2x-4y=2
3x+4y=8

Answers

To find if a point is a solution to a system of equations, we need to plug in the x and y values of the point into each equation, and see if the equation is true.

Let's plug it into the first equation first:

-2(3) - 4(-2) might = 2
-6 + 8 = 2

The first equation is true. 

Now, we need to check the second equation:

3(3) + 4(-2) might =8
9 - 8 does not = 8

Therefore, even if the point satisfies one equation, it does not satisfy the other. We can conclude that this is not a solution. 

Hope this helps!

108+621 is the same as 100+ what

Answers

I think the answer you looking for is 629

A cab driver is paid $6 plus $0.45 per mile driven. Which expression shows the amount of money the cab driver earns in m miles?

Answers

No expressions are showing to choose from, but it should look like:

A= amount of money earned
m= # of miles driven

Amount earned equals $6 plus ($0.45 times the # of miles driven.)

EQUATION:
A= $6 + $0.45m

Hope this helps! :)

Answer:

C/ 0.45m + 6

Step-by-step explanation:

i did the quiz

The legs of a right triangle are 12 cm and 16 cm. What is the length of the hypotenuse? 15 cm 17 cm 20 cm 28 cm

Answers

Answer: 20 cm

To solve this, use the Pythagorean Theorem, a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse of the right triangle.
**The Pythagorean Theorem only works for right triangles.**

Substitute in the values.
a² +  b² = c²
12² + 16² = c²

Solve for c, the hypotenuse.
12² + 16² = c²               
144 + 256 = c²
400 = c²
c = √400
c = 20

Answer:

20cm

Step-by-step explanation:

which of the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola is xy=4

Answers

try this option:
according to the equation it is a hyperbola.
The graph of this function is attached.
It's a hyperbola. The formula should be transformed into y = 1/x.

The value of Maggie's car decreased by 10% since last year, when she bought it. If the car is now worth $11,000.00, how much was the car worth when she bought it?

Answers

The value is decreased by 10%. This means that current price is 100%-10%=90% of the original price. Now we can solve this by using ratios

90%             $11000
100%           $x

Now we cross multiply numbers and solve it for x:
90*x = 100 * 11000
90x = 1 100 000
x= 1 100 000 / 90
x= $12 222,22

When Maggie bought a car theprice was $12 222,22

the figure shown is made up of a square and a triangle. Express the area of the figure in terms of y.

Answers

1. The figure is made up of a square and a triangle. Therefore, you can solve this problem by applying the formula for calculate the area of a square and the formula for calculate the area of a triangle.

 2. The area of the square (A1) is:

 A1=(y)(y)
 A1=y²

 3. The area of the triangle (A2) is:

 A2=(y)(4)/2

 4. When you simplify it, you obtain:

 A2=2y

 5. Finally, you obtain the area of the figure (A) when you sum the area of the square and the area of the triangle:

 A=A1+A2
 A=y²+2y 
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