log2 1 is defined
True
False

Step-by-step explanation:

am-an+bm-bn

m(a+b)-n(a+b)

(m-n)(a-b)

Answer:

[tex] \small \sf \: ( m - n ) ( a + b )[/tex]

Step-by-step explanation:

( am - an + bm - bn)

= ( am - an ) + ( bm - bn )

= a ( m - n ) + b ( m - n )

= ( m - n ) ( a + b )

Answer:

A = 24

Step-by-step explanation:

Figure shown is a trapezoid

Area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]

where a and b = base lengths and h = height

The trapezoid shown has the following dimensions

Shorter base length (a) = 6

Longer base length (b) = 10

Height (h) = 3

Using these dimensions , plug in the values into the area formula

A = [tex]\frac{6+10}{2} 3[/tex]

add 6 + 10 = 16

[tex]A=\frac{16}{2} 3[/tex]

divide 16/2 = 8

[tex]A = (8)(3)[/tex]

multiply 8 times 3

A = 24

Problem 27)

Refer to the diagram that says "problem 27".

This is the graph of y = 5x where x is the time in years, and y is the amount of simple interest in the account.

This equation comes from the simple interest formula below

i = P*r*t

i = 100*0.05*x

i = 5x

y = 5x

Note: The graph is a straight line through (0,0) and (1,5)

=====================================================

Problem 28)

The abscissa is the x coordinate. For a point like (-3, -7), the abscissa is -3.

The ordinate is the y coordinate. For that point mentioned earlier, the ordinate is -7.

The graph of points is shown below in the figure labeled "problem 28".

When graphing any point, we always start at the origin (0,0) where the x and y axis meet up. Then for a point like (-3,-7) we move 3 units to the left on the x axis and 7 units down on the y axis to arrive at point A. The other points are plotted in a similar fashion. The labels A,B,C,D are optional. They were added to help keep track of the points.

Answer:

an irrational number

Step-by-step explanation:

Answer:

Irrational numbers

Step-by-step explanation:

First, to solve this question, we need to know what irrational numbers are. Irrational numbers are numbers that cannot be expressed as a simple fraction. A nonterminating decimal cannot be expressed as a simple fraction, therefore making it an irrational number.

Hope this helps!

Answer:

x = 48-32 = 16

y = 32/16 × 10 = 20

z = 48/32 × 26 = 39

Answer:

(0,8)

Step-by-step explanation:

Let X be 0 and solve for Y to get the intercept

y= - 4([tex]10^{x}[/tex]) + 12

y= - 4 * [tex]10x^{0}[/tex] + 12

y= - 4 * 1 + 12

y= - 4 + 12

y=8

when x=0, y=8

(0,8) is y intercept

The y-intercept of the given function is (0,8).

We have given that,

The graph of the function f(x) = 10^x

The y-intercept of function gif g(x)=4f(x) + 12

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Let X be 0 and solve for Y to get the intercept

[tex]y= - 4(10^x) + 12[/tex]

[tex]y= - 4 (10^0) + 12[/tex]

[tex]y= - 4 * 1 + 12[/tex]

[tex]y= - 4 + 12[/tex]

[tex]y=8[/tex]

when x=0, y=8

The y-intercept of the given function is (0,8).

To learn more about the intercept visit:

https://brainly.com/question/1884491

#SPJ5

Answer:

70,000 - 20,000= 50,000

Answer:

BC ≈ 9.9 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin64° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{11}[/tex] ( multiply both sides by 11 )

11 × sin64° = BC , then

BC ≈ 9.9 cm ( to 1 dec. place )

Answer:

D: 2y = 8x - 10  

Step-by-step explanation:

A:  y = 4x + 5. This has a slope of -4 Yes it could work.

B:  y = 4x - 5. No It does not work

C: 2y = 8x - 10. The slope is 8/2 = 4. So No it could not work.

D: -2y = 8x - 10. The slope is 8/-2 = -4. Yes This Does work!  :)

Answer:

15.4 units

Step-by-step explanation:

sqrt(5²+4²) = sqrt(41) = 6.4

the other two legs are 5 and 4

so perimeter

= 4+5+6.4 = 15.4 units

Answer:

Science is more interesting for me than math and fun!

Step-by-step explanation:

Answer:

Math is more fun for me because you get to learn more stuff in it. Plus, math can help you in everyday stuff like for example cooking.

Step-by-step explanation:

Everyone agrees that learning math can be difficult, but some people believe math is important and some people believe math is not important. Math is important for three reasons: math is everywhere, children need math, and God created math.

The first reason math is important is math is everywhere. Math is used in everyday life; it is useful, but it is more than just useful. Math is there to help us, to keep us well ordered, to help us learn new things, and to help us teach new things. Students will become adults who will use math in their jobs. All kinds of careers use math; for example, musicians, accountants, fashion designers, and mothers use math. However, math is not only used for things you do. It also brings order to everything around you; the world is organized essentially because it was made with math.

The second reason math is important is children need math. Now, as we all know, children are as chaotic as a volcanic eruption, but children, as they grow, need to learn patience. Patience is precisely what math teaches us. It also teaches us curiosity; for example, why is this rule used here? Why would that number be negative? Why is that equation set up like that? These are questions they will learn to ask if they are taught math. The parents’ job is to help their children grow up to become good people who are patient and wise, who want to learn even more about anything and everything. Their future depends on what they have learned and if they have learned mathematics, then they will be able to do many different things—maybe even anything—when they are adults.

The third reason math is important is God created it. This is a reason most adults use to convince their children that math is not boring and unimportant, so it may seem unoriginal. I believe, however, it is something that needs to be stated. God created the universe as well as math. The universe is full of math and it is orderly because of math. The sun is a certain distance from the earth; everything is organized in such a way that no matter what has happened we have always been safe. We need math. From this, you should be able to see how much we really do use and need math. We would not be able to process or even do everyday things without it. Math, in addition to these things, helps us to know God. God gave us math to live well and to serve Him. With everything we learn using math in science, we learn more about the world, which can help draw us closer to God.

Some people say math is unimportant because you don’t need math other than basic math principles—you can live without more complicated math. They say, if you need it, then simply use a calculator and leave the more complicated math to people who like math, the mathematicians. This, however, is not correct; you need math and could not live well without math, even including more complicated math concepts. God made us with a sense of curiosity so we can learn, do, and think about all sorts of things. Math is that thing that connects everything together, everything people love to do: music, cooking, painting, and everything else. Math is important.

Math is important because math is everywhere, children need math, and God created math. This matters to me and other children because math determines our future and how we choose to live.

Answer:

2%

60/3000g= ?/100

60×100/3000=2

Answer:

100

Step-by-step explanation:

Based on the histogram given :

The vertical axis gives the number of student in the school :

For the range :

0 - 5 = 40

5 - 10 = 30

10 - 15 = 20

15 - 20 = 5

20 - 25 = 3

25 - 30 = 2

Taking the sum :

(40 + 30 + 20 + 5 + 3 + 2) = 100

Answer:

8 ≤t≤16

We know the low temperature was 8

8≤ t

And the high was 16

8 ≤t≤16

Step-by-step explanation:

5 + ( 2 × 42 ) =

5 + 84 =

89

.....

.....

Answer:

89

Step-by-step explanation:

So we will follow PEMDAS in this exact order:

P- Parentheses

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction

5 + 2 • 42 Equation

5 + (2 • 42) We have no parentheses or exponents so we move on to multiplication

5 + 84 We have no division so we move on to addition

= 89 We have no subtraction so this is our final answer

Answer:

h(x) is the image after f(x) is horizontally stretched by a scale factor of 4

Step-by-step explanation:

Given

[tex]h(x) = \frac{1}{4}x^2[/tex]

[tex]f(x) = x^2[/tex]

Required

Compare h(x) to f(x)

We have:

[tex]h(x) = \frac{1}{4}x^2[/tex]

Substitute [tex]f(x) = x^2[/tex]

[tex]h(x) = \frac{1}{4}f(x)[/tex]

This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)

Answer:

30%

Step-by-step explanation:

Let's say he has 100% income

Spends 70%

Remaining=100-70=30%

Step-by-step explanation:

total percentage = 100%

total percentage spend = 70%

remaining percentage = 100% — 70% = 30%

Answer:

The circumference of the back wheel is 2.62 inches

Step-by-step explanation:

Given

[tex]d_1 = 5in[/tex] --- diameter of front wheel

[tex]d_1 : d_2 = 3:1[/tex] --- ratio of the diameters

Required

The circumference of the back wheel

First, we calculate the diameter of the back wheel.

We have:

[tex]d_1 : d_2 = 3:1[/tex]

Substitute: [tex]d_1 = 5in[/tex]

[tex]5in: d_2 = 3 : 1[/tex]

Express as fraction

[tex]\frac{d_2}{5in} = \frac{1}{3}[/tex]

Make [tex]d_2[/tex] the subject

[tex]d_2 =5in * \frac{1}{3}[/tex]

[tex]d_2 = \frac{5}{3}\ in[/tex]

So, the circumference (C) of the back wheel is:

[tex]C =\pi d[/tex]

[tex]C = 3.14 * \frac{5}{6}\ in[/tex]

[tex]C = \frac{3.14 * 5}{6}\ in[/tex]

[tex]C = \frac{15.7}{6}\ in[/tex]

[tex]C = 2.62\ in[/tex]

Answer:

7

Step-by-step explanation:

I got it correct on a test

Answer:

[tex]6x^2+11x+3[/tex]

Step-by-step explanation:

Area of a rectangle = length x width

[tex](2x+3)(3x+1) = ?[/tex]

[tex]6x^2+2x+9x+3[/tex]

Answer:

10.25

Step-by-step explanation:

26-7(2.25)=10.25

Answer:

$10.25 would be left over

Step-by-step explanation:

Hyunjin spends 7($2.25), or $15.75, for those 7 americanos.

To find out how much money he'd have left, we subtract this $15.75 from his $26, obtaining $10.25.

Answer:

A. the first possible case is always n = 1

Step-by-step explanation:

Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers

Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0

Therefore, the statement which is not true is that the first possible case is always n = 1

Answer:

p = 30, n = 7, a = 15

Step-by-step explanation:

Let's say that p is the amount of stuffies Peyton sold, n is the amount of stuffies Nathan sold, and a is the amount of stuffies Alexandra sold.

Peyton sold two more than four times the stuffies Nathan sold.

This means that: p = 2 + 4n (n = (p-2)/4)

Each stuffie was sold for $2.50. Together they fundraised $130.Alexandra sold half as many stuffies as Peyton.

This means that: a = p/2

Each stuffie was sold for $2.50. Together they fundraised $130.

This means that: 2.50p + 2.50n + 2.50a = 2.50(p + n + a) = 130

We can make the equation in terms of p by substituting a and n.

2.50(p + n + a)

= 2.50(p + (p-2)/4 + p/2)

= 2.50(4p/4 + (p-2)/4 + 2p/4)   [Make the p's have a denominator of 4]

= 2.50((4p + p - 2 + 2p)/4)

= 2.50((7p-2)/4)

= 5/2 * (7p-2)/4

= 5(7p-2)/8

= (35p-10)/8 = 130

35p-10 = 1040

35p = 1050

p = 30

n = (30-2)/4

  = 7

a = 30/2

  = 15

Answer:

choice 4

Step-by-step explanation:

It's not that hard if you understand once you get past the fancy words

degree= largest exponent

so if something has a degree of 3 we know that the highest exponent is 3

Coeficcent= thing multipllying x

in this case it's 4 which means the number we are looking for is 4x³

Onlyanswer choice 4 meets these criteria

Answer:

The answer is (4)  [tex]2x+x^{2} +4x^{3}[/tex].

Step-by-step explanation:

A leading coefficient is the coefficient of the term of highest degree in a given polynomial.  

A degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables).

The answer can be found when the polynomial is rearranged into standard form, and the standard form of the polynomial will look like [tex]4x^{3}+x^{2} +2x[/tex]. A polynomial is in standard form when the term with the highest degree is placed first, followed by the term which has the next highest degree, and so on.

Once the polynomial is in standard form, the leading coefficient is 4 and has a degree of 3. Thus, causing (4) [tex]2x+x^{2} +4x^{3}[/tex] to be the answer.

Answer:

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Step-by-step explanation:

For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A company manufactures fuses. The percentage of non-defective fuses is 95.4%.

This means that 100 - 95.4 = 4.6% = 0.046 are defective, which means that [tex]p = 0.046[/tex]

A sample of 9 fuse was selected.

This means that [tex]n = 9[/tex]

Calculate the probability of selecting at least 3 defective fuses.

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{9,0}.(0.046)^{0}.(0.954)^{9} = 0.6545[/tex]

[tex]P(X = 1) = C_{9,1}.(0.046)^{1}.(0.954)^{8} = 0.2840[/tex]

[tex]P(X = 2) = C_{9,2}.(0.046)^{2}.(0.954)^{7} = 0.0548[/tex]

Then

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6545 + 0.2840 + 0.0548 = 0.9933[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.9933 = 0.0067[/tex]

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Answer:

Graph translates 4 units to the left then 3 units up.

Step-by-step explanation:

The constant in the bracket changes for - 15 to -11 . A change of + 4.

This shifts  the whole graph horizontally 4 units to the left.

The + 3 moves the whole graph 3 units upwards.

Answer:

Imaginary: 20i

Real: 26

Step-by-step explanation:

Hope this helped.

Answer:

(4,0)

Step-by-step explanation:

Line segment EG is partitioned by point F in the ratio 1:3.

This means that:

[tex]F - E = \frac{1}{4}(G - E)[/tex]

We use this equation to find both the x-coordinate and the y-coordinate of point G.

x-coordinate:

x-coordinate of E: 0

x-coordinate of F: 1

x-coordinate of G: x

Then

[tex]F - E = \frac{1}{4}(G - E)[/tex]

[tex]1 - 0 = \frac{1}{4}(x - 0)[/tex]

[tex]1 = \frac{x}{4}[/tex]

[tex]x = 4[/tex]

y-coordinate:

y-coordinate of E: 4

y-coordinate of F: 3

y-coordinate of G: y

Then

[tex]F - E = \frac{1}{4}(G - E)[/tex]

[tex]3 - 4 = \frac{1}{4}(y - 4)[/tex]

[tex]-1 = \frac{y-4}{4}[/tex]

[tex]y - 4 = -4[/tex]

[tex]y = 0[/tex]

What are the coordinates of point G?

x = 4, y = 0, so (4,0).