Answer: 3 people ordered soup.
Step-by-step explanation:
Let x be the number of people ordered salad and y be the number of people ordered soup.
As per given,
x=2y (i)
7.50x+6.25y= 63.75 (ii)
Substitute value of c =2y in (ii) , we get
7.50(2y)+6.25y= 63.75
⇒ 15y+6.25y = 63.75
⇒21.25y = 63.75
⇒ y= 3 [divide both sides by 21.25]
Then, x= 2(3) =6
So 6 people ordered salad and 3 people ordered soup.
15 POINTS!!!! BRAINLIEST FOR THE FIRST ANSWER!!! Solve 3-x/2≤18
Answer:
[tex]x\geq -30[/tex]
Step-by-step explanation:
Work to isolate x on one side of the inequality:
[tex]3-\frac{x}{2} \leq 18\\3-18\leq \frac{x}{2} \\-15\leq \frac{x}{2}\\-30 \leq x[/tex]
Therefore the answer is all x values larger than or equal to -30
[tex]x\geq -30[/tex]
Select the correct answer.
Write an expression to represent the sum of three times the square of a number and -7.
In your expression, what is the value of the constant?
O A 1
B. 2
Oc.
w
OD
-7
Reset
Next
Answer:
D. -7
Step-by-step explanation:
Sum of three times the square of a number and -7.
If we call the number x, then the expression is:
3x² - 7Here - 7 is constant, x is variable, 3 is coefficient
Correct answer choice is: D. -7
Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9.
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
The amount of garbage, G, produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured in thousands of people.
The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function f.
Explain the meaning of the statement f(5) = 2.
Answer:
the expression of the information in terms of function f is:
13 = f(40)
The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.
Step-by-step explanation:
suppose G and p are the two unknowns variables.
where;
G is measured in tons per week and:
p is measured in thousands of people.
∴
The relation between the amount of garbage produced by a city with population p can be expressed as:
G = f(p)
However;
The town of Tola has a population of 40,000 and produces 13 tons of garbage each week.
The objective is to express the information in terms of the function f.
So, if there is a population of 40,000 person in the town,
since p is measured in person per thousand and the value of garbage produced is 13 tons per week.
∴ the expression of the information in terms of function f is:
13 = f(40)
Explain the meaning of the statement f(5) = 2.
The given statement implies that
P which is measured in thousand people = 5
and the value of the garbage produced is 2.
SO , we can say that;
The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.
The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10 (-8/2)^2 = 16 What is the function written in vertex form? A.f(x) = 3(x + 4)2 – 6 B.f(x) = 3(x + 4)2 – 38 C.f(x) = 3(x – 4)2 – 6 D.f(x) = 3(x – 4)2 – 38
Answer:
D
Step-by-step explanation:
Given
f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x
= 3(x² - 8x) + 10
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term )² to x² - 8x
f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10
= 3(x - 4)² - 48 + 10
= 3(x - 4)² - 38 ← in vertex form → D
Answer:
d
Step-by-step explanation:
Find the value of x. Please help ASAP
Answer:
4
Step-by-step explanation:
(10-x)/x=3/2
so 2*(10-x)=3x
20-2x=3x
+2x +2x
20=5x
x=20/5
x=4
verify
(10-4)/4=3/2
6/4=3/2
TRUE
Suppose your cell phone carrier charges you a monthly fee of $30.00 for up to 300 minutes and $0.45 for each additional minute after the first 300. Assuming you used your phone for x minutes with x > 300, the total monthly fee would be
Answer: Need more info. We need to know how many minutes over the 300 minutes were used in order to calculate the correct monthly fee.
Step-by-step explanation:
Two statistics teachers both believe that each has the smarter class. To put this to the test, they give the same final exam to their students. A summary of the class sizes, class means, and standard deviations is given below:n1 = 47, x-bar1 = 84.4, s1 = 18n2 = 50, x-bar2 = 82.9, s2 = 17Is there evidence, at an ?=0.04 level of significance, to conclude that there is a difference in the two classes? Carry out an appropriate hypothesis test, filling in the information requested.How do I find the standardized test statistic and the p-value?Your decision for the hypothesis test: A. Do Not Reject H0. B. Do Not Reject Ha. C. Reject H0. D. Reject Ha.
Answer:
We conclude that there is no difference between the two classes.
Step-by-step explanation:
We are given that two statistics teachers both believe that each has a smarter class.
A summary of the class sizes, class means, and standard deviations is given below:n1 = 47, x-bar1 = 84.4, s1 = 18n2 = 50, x-bar2 = 82.9, s2 = 17
Let [tex]\mu_1[/tex] = mean age of student cars.
[tex]\mu_2[/tex] = mean age of faculty cars.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that there is no difference in the two classes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that there is a difference in the two classes}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t_n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years
[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years
[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years
[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years
[tex]n_1[/tex] = sample of student cars = 110
[tex]n_2[/tex] = sample of faculty cars = 75
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(47-1)\times 18^{2}+(50-1)\times 17^{2} }{47+50-2} }[/tex] = 17.491
So, the test statistics = [tex]\frac{(84.4-82.9)-(0)}{17.491 \times \sqrt{\frac{1}{47}+\frac{1}{50} } }[/tex] ~ [tex]t_9_5[/tex]
= 0.422
The value of t-test statistics is 0.422.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_9_5[/tex] > 0.422) = From the t table it is clear that the P-value will lie somewhere between 40% and 30%.
Since the P-value of our test statistics is way more than the level of significance of 0.04, so we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.
Therefore, we conclude that there is no difference between the two classes.
Write an integer to describe each situation: The Stock market increased by 75 points.
Answer:
The stock market increased 75 point: 75 or +75
Answer:
The stock market increased by 75 so your answer according to my understanding is +75 or 75.
Step-by-step explanation:
Hope it will help you :)
Roger bowled 7 games last weekend. His scores are 155, 165, 138, 172, 127, 193 , 142. What is the RANGE of Roger's scores?
Answer:
66
Step-by-step explanation:
In statistics, the formula for RANGE is given as the difference between the Highest and the Lowest value.
In the above values we are given data consisting of the 7 games that Roger bowled.
155, 165, 138, 172, 127, 193 , 142.
Step 1
We arrange from the least to the highest.
127, 138, 142, 155, 165, 172, 193
Step 2
Lowest value = 127
Highest value = 193
Step 3
Range = 193 - 127
= 66
Therefore, the range of Roger's scores is 66
find the unknown angle
Answer:
y= 75
x= 53
Step-by-step explanation:
y= 75
Vertically opposite angles
x=53
75 + 52 = 127
angles in a triangle add up to 180
180 - 127 = 53
Hope this helps!
♣ GIVEN ♣
A triangle is given to us.In that triangle two sides are produced.Two angles are given as variables and one of the angle is 52°.The angle formed by two produced sides is 75°.♣ TO FIND ♣
The two unknown angles.♣ SOLUTION ♣
In the given figure y = 75° , since y and 75° are Vertically opposite angles and vertically opposite angles are equal to each other.
Now , we know that the angle sum property of a ∆ is 180°, i.e. sum of all interior angles of a triangle is equal to 180°.
So , in the given ∆ ,
=> x + y + 52° = 180° .
=> 75° + 52° + x = 180°.
=> 127° + x = 180° .
=> x = (180 - 127)°.
☞ x = 53° .
Hence ,
x = 53°.y = 75°.I need an answer. online school sucks.
Answer:
98
Step-by-step explanation:
Answer:
98
Step-by-step explanation:
what pair of numbers is relatively prime
Answer:
Hi
Step-by-step explanation:
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
x^2−4x−21 I need help with this question and please right every step of it
Answer:
[tex] \boxed{ \boxed{ \sf{ \bold{( x - 7)(x + 3)}}}}[/tex]Step-by-step explanation:
[tex] \sf{ {x}^{2} - 4x - 21}[/tex]
Here, we have to find the two numbers that subtracts to 4 and multiplies to 21
⇒[tex] \sf{ {x}^{2} - (7 - 3)x - 21}[/tex]
⇒[tex] \sf{ {x}^{2} - 7x + 3x - 21}[/tex]
Factor out X from the expression
⇒[tex] \sf{ x(x - 7) + 3x - 21}[/tex]
Factor out 3 from the expression
⇒[tex] \sf{x(x - 7) + 3(x - 7)}[/tex]
Factor out x-7 from the expression
⇒[tex] \sf{(x - 7)(x + 3)}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex]\boxed{\boxed{\bold{(x - 7)(x + 3)}}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 4x - 21 \\ {x}^{2} - 7x + 3x - 21 \\ x(x - 7) + 3(x - 7) \\ (x - 7)(x + 3)[/tex]
Our library has 3,489 non-fiction books, 8,617 fiction books and 1,240 reference books. If there are 564 students and each student borrows 6 books, how many books will be left in the library?
Answer:
9,962
Step-by-step explanation:
3,489+8,617+1,240=13,346
564*6=3,384
13,346-3,384=9,962
Two boxes have the same volume. One box has a base that is 5\text{ cm}5 cm5, start text, space, c, m, end text by 5\text{ cm}5 cm5, start text, space, c, m, end text. The other box has a base that is 10\text{ cm}10 cm10, start text, space, c, m, end text by 10\text{ cm}10 cm10, start text, space, c, m, end text. How many times as tall is the box with the smaller base?
Answer:
4times tall
Step-by-step explanation:
Volume of the boxes = Base area × height
Volume of the first box V1 = A1h1
Given the base of the first box to be 5cm, the base area:
A1 = 5cm×5cm = 25cm²
Volume of the first box V1 = 25h1... 1
Similarly, volume of the second box
V2 = A2h2
Given the base of the second box to be 10cm, the base area:
A2= 10cm×10cm = 100cm²
Volume of the second box
V2 = 100h2... 2
If the two boxes have the same volume, then V1 = V2
25h1 = 100h2
divide both sides by 25
25h1/25 = 100h2/25
h1 = 4h2
Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.
Answer:
4times tall
Step-by-step explanation:
Volume of the boxes = Base area × height
Volume of the first box V1 = A1h1
Given the base of the first box to be 5cm, the base area:
A1 = 5cm×5cm = 25cm²
Volume of the first box V1 = 25h1... 1
Similarly, volume of the second box
V2 = A2h2
Given the base of the second box to be 10cm, the base area:
A2= 10cm×10cm = 100cm²
Volume of the second box
V2 = 100h2... 2
If the two boxes have the same volume, then V1 = V2
25h1 = 100h2
divide both sides by 25
25h1/25 = 100h2/25
h1 = 4h2
Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.
Solve for s
y = SV - Sk^4
Answer:
S = y / (V - k⁴) where V ≠ k⁴
Step-by-step explanation:
y = SV - Sk⁴
y = S(V - k⁴)
S = y / (V - k⁴) where V ≠ k⁴
both the Galapagos islands and the island of Nauru are on the equator, but the Galapagos islands are at 90.30degrees West whereas the island of Nauru is at 166.56degrees East. how far is it from the Galapagos islands to Nauru traveling over the Pacific ocean along the equator, correct to the nearest km? A. list and explain each step used in solving the question. B. identify the teaching materials or methods used you want to use in understanding and solving the question. C. implement the steps in (A) to solve the question.
Answer: This is what i can do . i hope it helps:)
The angle between the longitude of the Galapagos Islands and that of Nauru is 90.30°+166.56°=256.86°.
We find the sum since these places have different longitude directions, but this is the major arc, and the minor arc will be 360°−256.86°=103.14°.
Angle between Galapagos Islands and 180°E/W = 180° - 90.30° = 89.70°
Angel between Nauru island and 180°E/W = 180° - 166.56° = 13.44°
Total angle between Galapagos Islands and Nauru = 89.70 ° + 13.44° = 103.14°.
Step-by-step explanation:
[tex]let \:\alpha \:be\:our\:teetah \\l = \frac{r \pi}{180 \°} \times \alpha \\\\= \frac{6400\pi}{180 \°} \times 103.14\\\\= 11520.848\\\\= 11521 km[/tex]
Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning?
Answer:
0.0075
Step-by-step explanation:
According to the given situation, the calculation of the probability that the TPMS will trigger a warning is shown below:-
The tire pressure which is 26% below the target pressure is
[tex]= 26\% \times 28[/tex]
= 7.28
Therefore, Tire pressure monitoring systems warn at below is
= 28 - 7.28
= 20.72
Now we will assume tire pressure be x
So,
[tex]P(X<20.72) = P(\frac{X-\mu}{\sigma}<\frac{20.72-28}{3} )[/tex]
After solving the above equation we will get
= [tex]P(X<20.72) = P(Z<-2.43)[/tex]
we will get
= 0.0075
Simplify -k^2-(3k-6n)+2n when k=-3 and n=-5
Steps to solve:
-k^2 - (3k - 6n) + 2n; k = -3, n = -5
~Substitute ans simplify
-(-3)^2 - (3(-3) - 6(-5)) + 2(-5)
3^2 - (-9 + 30) - 10
~Use PEMDAS and solve the rest
9 - 21 - 10
-13 - 10
-23
Best of Luck!
Answer:
-2
Step-by-step explanation:
-(-3)∧2-(-9+30)+10= 9+9-30+10= -2
How can you move just one number to a different
triangle to make the sum of the numbers in each
triangle equal? (Hint: There do not have to be
exactly 3 numbers in each triangle.)
Answer:
Remove 9 from triangle B to A
Step-by-step explanation:
Given
Three Triangles
A: 1,2,3
B: 7,8,9
C: 4,5,6
Required
Make their sum equal
First, we need to calculate the sum in each triangles;
[tex]A = 1 + 2 + 3[/tex]
[tex]A = 6[/tex]
[tex]B = 7 + 8 + 9[/tex]
[tex]B = 24[/tex]
[tex]C = 4 + 5 + 6[/tex]
[tex]C = 15[/tex]
Remove 9 from triangle B to A
[tex]A = 6 + 9[/tex]
[tex]A = 15[/tex]
[tex]B = 24 - 9[/tex]
[tex]B = 15[/tex]
At this point, we have:
[tex]A = 15[/tex] [tex]B = 15[/tex] [tex]C = 15[/tex]
Hence, the solution is to remove 9 from B to A
What is the solution to the equation StartFraction x Over 3 EndFraction + StartFraction x Over 6 EndFraction = seven-halves? x = Three-halves x = Seven-thirds x = 3 x = 7
Answer:
x=7
Step-by-step explanation:
took the test
The required solution of the equation is x = 7.
Given that,
Solution of the equation,
x / 3 + x / 6 = 7 / 2 is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the equation?
The equation is the relationship between variables and represented as y = ax + b is example of a polynomial equation.
Here,
x / 3 + x / 6 = 7 / 2
Taking LCM on the left side
[2x + x] /6 = 7 / 2
3x / 6 = 7 / 2
x / 2 = 7 / 2
x = 7
Thus, the required solution of the equation is x = 7.
Learn more about arithmetic here:
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An is mathematical sentence that compares expression that are not equal
Answer:
Inequality
Step-by-step explanation:
An inequality is mathematical sentence that compares expression that are not equal.
Instead of using an equal sign = , you use an inequality symbol (>, <, ≥, ≤, ≠) with an inequality.anyone know dis one pls
Answer:
A - the arrow on the right points to the point -2. the arrow on the left moves 7 places to the left to the point -9.
this is what the expression is stating: -2 - 7 = -9
You are planning to invest $5000 in an account earning 9% per year for retirement. a. If you put the $5000 in an account at age 23, and withdraw it 42 years later, how much will you have? b. If you wait 10 years before making the deposit, so that it stays in the account for only 32 years, how much will you have at the end?
Answer:
A).Amount = $218250
B). Amount = $88700
Step-by-step explanation:
A) .$5000 in an account at age 23, and withdraw it 42 years
Number of years t= 42 years
Principal P = $5000
Rate r= 9%
Number of times compounded n= 42
A= p(1+r/n)^(nt)
A= 5000(1+0.09/42)^(42*42)
A= 5000(1+0.002143)^(1764)
A= 5000(1.002143)^1764
A= 5000(43.65)
A= 218250
Amount = $218250
B).waits 10 years before making the deposit, so that it stays in the account for only 32 years
Number of years t= 32 years
Principal P = $5000
Rate r= 9%
Number of times compounded n= 32
A= p(1+r/n)^(nt)
A= 5000(1+0.09/32)^(32*32)
A= A= 5000(1+0.0028125)^(1024)
A= 5000(1.0028125)^1024
A= 5000(17.74)
A= 88700
Amount = $88700
A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1800 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
The first car used 30 gallons and the second one 20 gallons of gas during the trip.
Step-by-step explanation:
35x+40y = 1850 equation 1
x+y = 50 equation 2
x=car 1
y=car 2
Solve it
If
4²+3²/4²−3² =7/4
, find the value of
24−11⁴/24+11⁴
Solve using PEMDAS for the numerator and denominator.
24-11^4/24+11^4
24-14641/24+14641
-14617/14665
Best of Luck!
You decide you need a new computer. The cost of the computer is $768. However,
the store also offers a rent to own option which will cost $37 per week for 24 weeks.
How much more will the rent to own option cost after you have made all of the
payments? S
Answer:32
Step-by-step explanation:
768/24=32
The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.
What is a rent-to-own contract?A rent-to-own contract is a contract where the buyer pays for something as rent to the owner until the set period in the contract.
How to solve the given question?In the question, we are informed that a person decides to buy a new computer. He has two options to buy. Either he can pay the full cost of the computer = $768, or he can choose a rent-to-own option, in which he will pay $37 per week for 24 weeks.
We are asked to find the extra cost that the person will pay if he chooses the rent-to-own option, after completing all his payments.
The total amount that the person pays in the rent-to-own option = $37*24
or, the total amount that the person pays in the rent-to-own option = $888.
The actual cost of the computer = $768.
∴ Extra payment = Total Payment - Actual cost
or, Extra payment = $888 - $768 = $120.
∴ The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.
Learn more about a rent-to-own contract at
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Write a polynomial in standard form with the zeros -4,0, 1, and 4.
A. x4 – x3 - 8x2 + 16x
B. x4 – x3 – 16x2 + 16x
C. X4 - 7x3 + 8x2 + 16x
D. x4-9x3 + 24x2 – 16x
Answer: [tex]x^4-x^3-16x^2+16x[/tex]
Step-by-step explanation:
Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).
Given: Zeroes of polynomial : -4,0, 1, and 4.
Then Factors = [tex](x-(-4)), (x-0), (x-1) and (x-4)[/tex] [By factor theorem ]
[tex]=(x+4), (x-0), (x-1) and (x-4)[/tex]
Multiplying these factors to get polynomial in standard form.
[tex](x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x[/tex]
Hence, B is the correct option.
Laryngeal cancer rates in smokers is 160.0 (per 100,000) and 25.0 (per 100,000) among nonsmokers. Among smokers, what percentage of laryngeal cancer cases are due to the exposure (smoking)?
Answer:
0.16%
Step-by-step explanation:
From the statement of the question;
Number of Laryngeal cancer due to smoking = 160
Population of smokers = 100,000
Hence the percentage of smokers liable to have Laryngeal cancer = 160/100000 ×100/1
=0.16%
Hence 0.16% of smokers are liable to Laryngeal cancer