Answer:
102 sodas63 hot dogsStep-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.
find the area of a triangle with the given base and height
7ft, 2in
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
which is equivalent to the following expression (3m^2+2mn-n^2)+(m^2+4mn-n^2)
Answer:
4m² + 6mn - 2n²Step-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.
How the equivalent expression is determined?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.
Learn more about Equivalent Expression here: https://brainly.com/question/2972832
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please help me. math.
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
If you flip a coin 44 times what is the best prediction possible for the number of times it’ll land on heads
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.
There are 120 girls and 102 boys in 6th grade at Travis Intermediate. If 17 boys are in the first PE class, how many girls are likely in that class?
A
120 girls
B
22 girls
C
17 girls
D
20 girls
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
Which is closest to the value of x
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.
Write a sentence to represent the equation 4 m = -8.
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.
A set of n = 15 pairs of scores (x and y values) has ssx = 4, ssy = 25, and sp = 6. what is the pearson correlation for these data? 6/100 6/10 6/(100/15)
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
Write an equation that gives the proportional relationship of the graph.
A)
y = 1/6x
B)
y = 2x
C)
y = 6x
D)
y = 12x
C) y = 6x
Step-by-step explanation: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
Prove that u(n) is a group under the operation of multiplication modulo n.
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.
For the function f(x)= log5 3x-10 explain why x=2 is not in the domain
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.
A company manufactures skateboards. Each skateboard requires 1 6/7 hours of labor to assemble and 2 1/2 hours of labor to finish and stain. The cost of labor to the company is $36.00 each hour. Find the product 36\left(1\frac{6}{7}\ +\ 2\frac{1}{2}\right)36(1 7 6 + 2 2 1 ) using the distributive property. Describe what each individual term in the expression represents in the context of this situation after you distribute the 36, AND describe what the final result represents. Show your work, and explain
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.
Given: KLMN is a trapezoid, KL=MN, m∠1=m∠2, LM/KN = 8/9 , Perimeter KLMN=132 Find: The length of midsegment.
34
Step-by-step explanation: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.
Learn more about the concept of midsegments here:
https://brainly.com/question/2273557
find the exponential model of best fit for the points (-3,5),(1,12),(5,72),(7,137). Explian how you got your answer. Round values to the nearest hundredth.
f(x) = 11.93·1.42^x
Step-by-step explanation: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.
Can anyone help me with THIS and the other TWO‼️PLEASE I’m really need HELP
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