Answer:
[tex]\left\{\begin{matrix}2p + 4c = 31.50\\3p + 2c = 33.25\end{matrix}\right.[/tex]
Step-by-step explanation:
Let's call (as suggested)
p = the cost of one pizza
c = the cost of one cheeseburger
The Anderson Family ordered 2 pizzas and 4 cheeseburgers and paid $31.50, thus:
2p + 4c = 31.50 [1]
Next weekend, they ate at the same restaurant and ordered 3 pizzas and 2 cheeseburgers for $33.25, thus:
3p + 2c = 33.25 [2]
To know the cost of one pizza and one cheeseburger, we need to solve the system of equations defined by [1] and [2]
[tex]\left\{\begin{matrix}2p + 4c = 31.50\\3p + 2c = 33.25\end{matrix}\right.[/tex]
In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.
Find the common difference. Give only the exact value as your answer.
Answer:
37.5% that is the answer
Step-by-step explanation:
The required common difference is 4.
What is an arithmatic progression?An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
Now it is given that,
the seventh term, T₇ = −9 and
the nineteenth term, T₉ = 39.
Let a be the first term, d is the common difference and n is the number of term.
Since Tn of the series is given as,
Tn = a + (n-1)d
Therefore,
T₇ = a + (7-1)d
⇒ -9 = a + 6d ...(i)
and,
T₉ = a + (19-1)d
⇒ 39 = a + 18d ...(ii)
Subtracting equation (ii) by (i) we get,
48 = 12d
or, d = 48/12
⇒ d = 4
Thus, the required common difference is 4.
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. The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test. (Use
= 0.05.
Use 1 for Mexico and 2 for the United States.)
Answer:
Yes the conclusion in the question is a reasonable conclusion
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_1 = n_2 = n = 250[/tex]
The sample mean for USA is [tex]\= x_1 = 391 \ minutes[/tex]
The sample mean for Mexico is [tex]\= x_2 = 426 \ minutes[/tex]
The sample standard deviation for USA is [tex]s_1 = 25 \ minutes[/tex]
The sample standard deviation for Mexico is [tex]s_2 = 49 \ minutes[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 < \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }[/tex]
=> [tex]z = \frac{ 391 - 426 }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }[/tex]
=> [tex]z = -10[/tex]
From the z table the area under the normal curve to the left corresponding to -10 is
[tex]p-value = P(Z < -10 ) = 0.00[/tex]
Generally from the value obtained we see that
The p-value is < [tex]\alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico
Hence the conclusion in the question is a reasonable conclusion
The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis. This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.
Given :
The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night.For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes.Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample.According to the given data the sample size of the US and Mexico is [tex]\rm n_1=n_2=250[/tex].
The hypothesis are as follows:
Null Hypothesis is [tex]\rm H_0 : \mu_1=\mu_2[/tex]
Alternate Hypothesis is [tex]\rm H_1 : \mu_1<\mu_2[/tex]
Now, the mathematical representation of test statistics is:
[tex]\rm z = \dfrac{\bar{x_1}-\bar{x_2}}{\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}} }[/tex]
[tex]\rm z = \dfrac{391-496}{\sqrt{\dfrac{25^2}{250}+\dfrac{49^2}{250}} }[/tex]
z = -10
According to the z-table:
p - value = p (Z < -10) = 0
The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis.
This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.
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A bag of marbles contains three blue, one black, and four
yellow marbles. If two marbles are chosen at random
without replacement, what is the probability that both
marbles will be yellow?
Answer:
3/14Step-by-step explanation:
Blue = 3Black = 1Yellow = 4Total = 3 + 1 + 4 = 8
Probability of two yellows:
4/8*3/7 = 3/14Rob is setting up a model train track that is 3 and 3 over 8 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 3 over 8 foot apart. How many telephone poles does he need? (Input number values only.
Answer:
9?
Step-by-step explanation:
Answer:
sorry dont understaand
Step-by-step explanation:
The sum of five times a number and four is equal to negative eleven. What is the number?
-4
-5
-2
-3
Answer:
-4
Step-by-step explanation:
Answer:
The answer is -3
Step-by-step explanation:
First I subtracted 4 from -11 giving me the product of 5 and n before 4 was added which is -15
I then divided -15 by 5 giving me -3
КУ Meccahi Grant Question #21 The perimeter of a rectangle is given by the algebraic Part A. expression 2x2 + 4x + 4. The width of this rectangle Create an algebraic expression in terms of x to 2 is given by the algebraic expression x? – 4. represent the length of the rectangle. The perimeter of a rectangle is given by the algebraic expression 2x2 + 4x +4. The width of this rectangle is given by the algebraic expression x2 - 4. Part A Create an algebraic expression in terms of x to represent the length of the rectangle. Part B If x = 3, what is the area of this rectangle in squa units? Remember to include units.
Answer: The question requires an understanding of how to compose and decompose multi digit numbers. The expanded form 70,000 + 4,000 + 70 + 2 corresponds to the number 74,072, which is the population of Davidson County.
(sorry if i'm wrong)
:(
Which container holds more, a half-gallon milk jug or a 2-liter juice bottle
Answer:
1 gallon=3.79 liters 2 liter juice bottle would hold more
Step-by-step explanation:
What is the difference between ploting (2, 3) and (3, 2)
on a coordinate plane? Explain.
Could someone answer this I am a bit confused I will give a brainlist for the right answer I promise :)
Answer:
NP=14
BC=44
Step-by-step explanation:
[tex]60-24-22=14\\NP=14\\MN=BP=PC\\BC=2(MN)\\BC=44[/tex]
Please answer, will give brainliest.
Answer:
third one
Step-by-step explanation:
Answer:
I think one solution
Step-by-step explanation:
*Sorry if this did not help. I'm only in 5th grade*
find the slope intercept form of the equation of the line that passes through (-1,5) and is parallel to the line y=2x+4
Answer:
y = 2x + 7
Step-by-step explanation:
Which number line correctly shows -3-(1.5)
Solve this equation 5x -7 = -12
Answer:
The answer is x = -1
Step-by-step explanation:
Answer:
x=-1
Step-by-step explanation:
5x-7=-12
5x=-5
x=-1
If a wagon is accelerating at a rate of 2 m/s and the
force acting on it is 20 N, what is the mass of the
wagon?
Answer:
40kg
Explanation:
a=2m/s^
f=20N
M=?
we know
f=m*a
or, 20=m*2
or, 2m=20
or, m= 20/2
:. m=10 kg
Please helpp I’ll give brainleist
Answer:
87 for lo and om is 56
Step-by-step explanation:
Answer:
<LON= 98 Degrees
Step-by-step explanation:
180-55(2)=70
70+28=98
A classroom is painting the classrooms. Each classroom takes 1/3 of a gallon of
paint. If the school buys 6 gallons of paint, how many classrooms can they paint?
Plz help
Answer: try 18
Step-by-step explanation:
For every 24 cookies, there are 12 students. Which ratio does not represent cookies to students?
Answer: 12:24
Step-by-step explanation:
You can’t have 12 students to each cookie
Answer:
D: 2 students for every cookie
Step-by-step explanation:
D does not represent the ratio of cookies to students because it claims there are 2 students to every cookie, where there are 2 cookies for every student.
4(2x-15)+7(3x+2)=70?
Answer:
the answer is [tex]x=4[/tex]
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps :)
Simplify:
3^x-1 × 27^x+1
___________
81^x
Answer:
3^x-1×27^x+1
___________
81^x
81^x+x-1+1
_________
81^x
81^2x
_____
81^x
81^2x-1x
81^1x
Simplify 18 - 6x + 5x - 11
Answer:
7-x
Step-by-step explanation:
18-11=7
-6x+5x=-x
therefore, the answer is 7-x
The solution of the expression is,
⇒ - x + 7
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 18 - 6x + 5x - 11
Now, We can solve the expression as;
⇒ 18 - 6x + 5x - 11
Rearrange as;
⇒ - 6x + 5x + 18 - 11
Combine like term as;
⇒ - x + 7
Thus, The solution of the expression is,
⇒ - x + 7
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which point of the number line represents negative 4/5?
A
B
C
D
Answer:
the answer is A
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST
Does the following table represent a linear function? If so, find the linear equation that models the data.
please help UwU
if correct you get Brainiest
Answer: C
Step-by-step explanation:
(b) 25% of what number is 17?
Answer:
68
Step-by-step explanation:
derive that 25 percent of 68 equals 17.
Answer:
25 percent of 68 equals 17.
Step-by-step explanation:
Sally used 5 gallons of ginger ale, 1 gallon of orange juice, and 2 gallons of pineapple juice, to make a punch for her family holiday party. How many
quarts of punch will Sally have for her party?
32 quarts
52 quarts
O 36 quarts
12 quarts
Answer:
A.) 32 quarts
Step-by-step explanation:
If there are 4 quarts in a gallon, and Sally has 8 gallons of punch total, 4*8=32 quarts.
Answer:
32 quarts
Step-by-step explanation:
1 gallon = 4 quarts
5+1+2=8
8 × 4 = 32
For f(x) = x3-x2, which gives an output of 48?
A. f(-8)
B. f(-4)
C. f(4)
D. f(8)
Answer:
The input is x−2, therefore
Step-by-step explanation:
f(x−2)=(x−2)2−3(x−2)+1
easy question if your having big problem
Answer:
whats the problem
Step-by-step explanation:
Answer:
yup
Step-by-step explanation:
Write a cubic function whose graph is shown
Answer:
f(x) = x³ - 2x² - x + 2
Step-by-step explanation:
Since, the graph attached has three zeros (x-intercepts) at x = -1, 1 and 2,
Equation of the given function will be,
f(x) = (x + 1)(x - 1)(x - 2)
By solving this equation,
f(x) = (x² - 1)(x - 2)
= x²(x - 2) - 1(x - 2)
= x³ - 2x² - x + 2
Therefore, answer will be f(x) = x³ - 2x² - x + 2.
According to the given graph,
Three zeros,
x = -1, 1, and 2The function will be:
→ [tex]f(x) = (x+1)(x-1)(x-2)[/tex]
By solving this, we get
[tex]= (x^2-1)(x-2)[/tex]
[tex]= x^2(x-2)-1(x-2)[/tex]
[tex]= x^3-2x^2-x+2[/tex]
Thus the function above is right.
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Mrs. Savino runs 3 miles in 28 minutes. At this rate, how many minutes would it take her to run 15 miles? * Need it ASAP
Answer:
she would take 140 minutes to run 15 miles
Step-by-step explanation:
28 X 5 os equal to 140
Answer:
139.95
Step-by-step explanation:
28 divided by 3 is 9.33 so 9.33x 15=139.95
HELP ME PLEASEEEEEEEEEE