From 1994 to 1995 the sales of a book decreased by 80%. If the sales in 1996 were the same as in 1994, by what percent did they increase from 1995 to 1996?

f(x) = -(x -2)² +3

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3

Answer:

The difference is 18.7 degrees

Step-by-step explanation:

To find the difference in the temperature, we take the high temperature and subtract the low temperature.

Difference = high - low

                   = -3.6 - (-22.3)

                   = -3.6+22.3

                   = 18.7

The difference is 18.7 degrees

Answer:

Step-by-step explanation:

[tex](3m^2+2mn-n^2)+(m^2+4mn-n^2)\\\\=3m^2+2mn-n^2+m^2+4mn-n^2\qquad\text{combine like terms}\\\\=(3m^2+m^2)+(2mn+4mn)+(-n^2-n^2)\\\\=\boxed{4m^2+6mn-2n^2}[/tex]

Based on the available information, the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

To simplify the expression (3m² + 2mn - n²) + (m² + 4mn - n²), we can combine like terms.

Like terms have the same variables and the same exponents.

Let's group the like terms together:

(3m² + m²) + (2mn + 4mn) + (-n²- n²)

Combining like terms within each group, we get:

4m² + 6mn - 2n²

Therefore, in this case, it is concluded that the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

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Answer:

11

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that

... Cos = Adjacent/Hypotenuse

so you know ...

... cos(41°) = x / 14

Multiplying by 14 gives the value of x.

... x = 14·cos(41°) ≈ 10.566 ≈ 11

_____

Comment on answer choices

The visible answers are 10, 40, 12. The best choice of those is 10. If there is no choice offering 11 as the answer, then I'd choose 10.

Answer:

11

Step-by-step explanation:

Here we are given a right angled triangle with a known angle of 41°, length of the hypotenuse to be 14 and we are to find the length of the base x.

For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.

[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]

So putting in the given values to get:

[tex]cos 41=\frac{x}{14} \\\\x= cos 41*14\\\\x=10.56[/tex]

Therefore, the value of x is the closest to 11.

Answer:

The product of 4 and m is -8.

Without numbers: The product of four and the variable m is negative eight.

Step-by-step explanation:

4m means m is multiplied by 4. The result of the multiplication operation is called a "product." The equal sign translates to "is".

The sentence 'Four times a certain number equals negative eight' corresponds to the equation 4m = -8, indicating that multiplying a number by four yields negative eight.

The sentence to represent the equation 4 m = -8 might be: "Four times a certain number equals negative eight." This sentence encapsulates the equation by specifying that the product of the number m and four is equivalent to negative eight, implying that m will have a negative value since it is equal to a negative number when multiplied by a positive.

C) y = 6x

Pick any point. It is often convenient to use x = 1 (no marked point) or x = 10 (where y = 60).

Use these values to see which equation agrees.

A: 60 ≠ (1/6)·10

B: 60 ≠ 2·20

C: 60 = 6·10

D: 60 ≠ 12·10

____

Or, you can solve ...

... y = kx

for k, using the point values you found on the graph.

... 60 = k·10

... 60/10 = k = 6 . . . . . divide by 10

This makes the equation be ...

... y = 6x . . . . . . matches selection C

Answer:

A =  84 inches^2

Step-by-step explanation:

We know that the formula for the area of a triangle is given by

A = 1/2 b*h

Let's substitute what we know

We need the units to be the same

Convert 7 ft to inches

1 ft = 12 inches

Multiply both sides by 7

7 ft = 84 inches

A = 1/2 *84*2

A =  84 inches^2

the answer is

1.  x=28

2. p=7

Answer:

12% chance of 22

35% chance of 21, 22, or 23

55% chance of 20, 21, 22, 23, or 24

How can 22 be a good prediction when it's wrong 88% of the time?

I'd say from 20 to 24 is a good prediction without being trivial.

Step-by-step explanation:

C(n,k) = n Choose k = n! / (k! (n-k)!)

aka binomial coefficient

aka from n things choose k

To get probability of getting heads 22 times in 44 tries, you divide number of ways to get heads 22 times by number of ways to assign heads or tails to each throw.

Two ways to assign H or T to first, times two ways for second throw,

gives 2^44. That's the denominator.

Number of ways to get heads 22 times is the same as number of ways to choose which 22 flips of 44 are to be heads, or C(44,22)

To get 12% calculate C(44,22)/2^44

To get 55% calculate C(44,20)/2^44 + ... + C(44,24)/2^44

Final answer:

The best prediction for the number of times a coin will land on heads after 44 flips is 22 times, as each flip has a 50-50 chance of resulting in heads.

Explanation:

When you flip a coin 44 times, the best prediction for the number of times it will land on heads is that it will land on heads about 22 times. This is because each flip is independent, and the probability of landing on heads is 50%, or a 50-50 chance.

When a coin is tossed multiple times, despite the possibility of getting streaks of either outcome, as the number of flips increases, the overall distribution of heads and tails tends to even out and approach a 50% split due to the law of large numbers. For example, if you tossed a coin 100 times, the number of heads and tails would be close to 50 each, although not exactly due to the randomness of each flip.

Answer:

Step-by-step explanation:

The simple answer is that logs cannot be negative and if you insert a 2 where the x is located you get a negative. Logs have to be >= 0

[text]log_5 (3x-10) = log_5 (-4)[tex]

It all has to do with logs being tied to exponents and exponents being tied to logs. Actually an inverse of an exponent is a log.

Answer:

We are given:

[tex]SSx = 4[/tex]

[tex]SSy=25[/tex]

[tex]Sp=6[/tex]

We know that the Pearson's correlation coefficient is:

[tex]r=\frac{S_{p}}{\sqrt{SS_{x} \times SS_{y}} }[/tex]

     [tex]=\frac{6}{\sqrt{4 \times 25} }[/tex]

     [tex]=\frac{6}{\sqrt{100} }[/tex]

     [tex]=\frac{6}{10}[/tex]

Therefore, the option 6/10 is correct

Answer: The total cost will be $156.85.

Step-by-step explanation:

Since we have given that

Time taken by labor to assemble the each skateboard is given by

[tex]1\frac{6}{7}\ hours\\\\=\frac{13}{7}\ hours[/tex]

Time taken by labor to finish and stain each skateboard is given by

[tex]2\frac{1}{2}\ hours\\\\=\frac{5}{2}\ hours[/tex]

Cost of labour to the company per hour = $36.00

According to question,

We will use "Distributive Property":

[tex]a\times (b+c)=a\times b+a\times c[/tex]

[tex]36(\frac{13}{7}+\frac{5}{2})\\\\=36\times \frac{13}{7}+36\times \frac{5}{2}\\\\=\frac{468}{7}+18\times 5\\\\=\frac{468}{7}+90\\\\=\frac{468+630}{7}\\\\=\frac{1098}{7}\\\\=\$156.85[/tex]

Hence, the total cost will be $156.85.

34

KM is a transversal relative to parallel lines LM and KN. Thus ∠2 = ∠MKN ≅ ∠KML and ∠KML = ∠1. The two base angles of ΔKLM are equal, so that triangle is isosceles.

Then the ratios of all the sides are ...

... KL : LM : MN : KN = 8 : 8 : 8 : 9

The sum of these ratio units is 33, so each one stands for 132/33 = 4 perimeter length units. Then segment LM is 8×4 = 32 perimeter length units, and KN is 9×4 = 36 permeter length units.

The midsegment is the average of lengths LM and KN, so is ...

... (32 +36)/2 = 34 . . . . perimeter length units

The length of midsegment is 34 units.

Given data:

The trapezoid KLMN, Such that KL = MN.

And [tex]m\angle1 = m\angle2[/tex], LM/KN = 8/9

Also, perimeter of KLMN = 132 units.

To find:

The length of midsegment (KM).

In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,

[tex]\angle MKN = \angle KML\\\angle 2=\angle 1\\[/tex]

Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.

Taking the ratios of sides of two triangles as,

= KL : LM : MN : KN

= 8 : 8 : 8 : 9

The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,

[tex]= \dfrac{perimeter}{33} \\\\=\dfrac{132}{33} \\\\=4[/tex]

Then the length of segment LM is,

[tex]LM = 8 \times 4 = 32 \;\rm perimeter \;\rm length \;\rm units[/tex]

And, length of segment KN is,

[tex]KN = 9 \times 4 = 36 \;\rm perimeter \;\rm length \;\rm units[/tex]

Then, the length of midsegment KM is obtained by taking the average of LM and KN as,

[tex]KM = \dfrac{LM+KN}{2} \\\\KM = \dfrac{32+36}{2}\\KE = 34[/tex]

Thus, the length of midsegment is 34 units.

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Answer:

Number of girls in PE class is 20

D.  20 girls

Step-by-step explanation:

We are given

Number of girls in 6th grade =120

Number of boys in 6th grade =102

so, firstly we will find ratios of girls and boys

[tex]\frac{G}{B}=\frac{120}{102}[/tex]

now, we have

17 boys are in the first PE class

Let's assume number girls in PE class as 'x'

we know that

ratios of boys and girls must be equal

so, we get

[tex]\frac{G}{B}=\frac{120}{102}=\frac{x}{17}[/tex]

now, we can solve for x

[tex]\frac{120}{102}=\frac{x}{17}[/tex]

[tex]x=17\times \frac{120}{102}[/tex]

[tex]x=20[/tex]

So,

Number of girls in PE class is 20

Answer:

y = 3x +2

Step-by-step explanation:

It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.

You are given the equation of a line in "slope-intercept" form. It looks like ...

... y = mx + b . . . . . . . where m=-1/3 and b=-1

The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.

The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...

...(m)(-1/3) = -1

... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.

____

Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...

... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)

We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...

... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form

The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.

... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property

... y = 3x +2 . . . . . . collect terms

The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.

___

*Comment on point-slope form

Usually, you will see "point-slope" form written as ...

... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form

When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...

... y = m(x -h) +k . . . . . . . occasionally useful version

f(x) = 11.93·1.42^x

I entered the data into a graphing calculator and made use of its exponential regression function to find the coefficients of ...

... y = a·b^x

It told me ...

... a ≈ 11.9304, b ≈ 1.41885

In accordance with the problem statement, these values are rounded to hundredths to get the answer.

_____

Comment on the graph

The given points and two curves are show. The solid red curve is the exponential regression curve produced by the calculator. The dotted blue curve is the one you get when you round the numbers to the nearest hundredth.

Answer:

Step-by-step explanation:

Let s and h represent the numbers of sodas and hotdogs sold, respectively. The problem statement tells you ...

... s + h = 165

... s - h = 39

Add these two equations to get ...

... 2s = 204

... s = 102 . . . . . divide by w

... h = 165 - 102 = 63 . . . . use the first equation to find h from s

The vendor sold 102 sodas and 63 hot dogs at the basketball game.

Answer:

-3367 1/9

Step-by-step explanation:

This is what calculators are for.

Perform the multiplication and division before the addition.

... = 10000/-9 -2256

... = -1111 1/9 -2256

... = -3367 1/9

_____

If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.

Answer:

y =293(1.06) ^x

y = 370  after 4 years

Step-by-step explanation:

If we are using the model for growth

y = a ( 1+b)^x

a is the initial population

b is  the increase rate

We can substitute the values into the equation

y =293 (1+.06) ^ x

y =293(1.06) ^x

Let x equal 4 for the 4 years

y = 293(1.06)^4

y=369.9

Answer:

The answer is the proof so it is long.

The question doesn't define u(n), but it's not hard to guess.

Group G with operation ∘

For all a and b and c in G:

1) identity: e ∈ G, e∘a = a∘e = a,

2) inverse: a' ∈ G, a∘a' = a'∘a = e,

3) closed: a∘b ∈ G,

4) associative: (a∘b)∘c = a∘(b∘c),

5) (optional) commutative: a∘b = b∘a.

Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.

If n isn't prime, we exclude from the group all integers which share factors with n.

Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).

Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).

Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.

Associative and Commutative:

(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)

a∘b = b∘a because ab = ba.

Answer:

The answer is the proof so it is long.

The question doesn't define u(n), but it's not hard to guess.

Group G with operation ∘

For all a and b and c in G:

1) identity: e ∈ G, e∘a = a∘e = a,

2) inverse: a' ∈ G, a∘a' = a'∘a = e,

3) closed: a∘b ∈ G,

4) associative: (a∘b)∘c = a∘(b∘c),

5) (optional) commutative: a∘b = b∘a.

Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.

If n isn't prime, we exclude from the group all integers which share factors with n.

Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).

Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).

Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.

Associative and Commutative:

(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)

a∘b = b∘a because ab = ba.

Answer:

21

Step-by-step explanation:

Simplify 5^2 to 25

25-2^2

Simplify 2^2 to 4

25-4

Answer

21

The value of the expression will be 21.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 5²- 2²

Simplify the expression, then the value of the expression will be given as,

⇒ 5²- 2²

⇒ 25 - 4

⇒ 21

The value of the expression will be 21.

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