Answer:
The null and alternative hypotheses are:
[tex]H_{0}: \mu = 170[/tex]
[tex]H_{a}: \mu >170[/tex]
Under the null hypothesis, the test statistic is:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
[tex]=\frac{180-170}{\frac{35}{\sqrt{225}} }[/tex]
[tex]=\frac{10}{2.33}[/tex]
[tex]=4.29[/tex]
Now, we have to find the right tailed z critical value at 0.10 significance level. Using the standard normal table, we have:
[tex]z_{critical} = 1.28[/tex]
Since the test statistic is greater than the z critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the university students weigh more than the population.
WILL GIVE BRAINLIEST
Which of the following is true about the decimal form of the number? 892/16
A.
It is a terminating decimal.
B.
It is neither a terminating decimal nor a repeating decimal.
C.
It is both a terminating decimal and a repeating decimal.
D.
It is a repeating decimal.
Answer:
The answer is A.
Step-by-step explanation:
When 892/16 was put into decimal form I ended up with 55.75.
That is a terminating decimal.
Terminating decimal ends after a few number of digits.
Answer:
A
Step-by-step explanation:
In the cafeteria's refrigerator, there are 10 bottles of orange juice and 20 bottles of apple juice. What is the ratio of bottles of orange juice to bottles of apple juice in the cafeteria's refrigerator?
Answer:
1:2
Step-by-step explanation:
Because 10/20 = 1/2
Answer: 10,20
Step-by-step explanation:
30°-60°-90° special triangle. how do I solve?
In the trinagle 30 - 60 - 90 the sides are in proportion 1 : √3 : 2.
Look at the picture.
We have:
[tex]a=2\sqrt5[/tex]
Therefore
[tex]A=2a\to A=(2)(2\sqrt5)=4\sqrt5\\\\B=a\sqrt3\to B=(2\sqrt5)(\sqrt3)=2\sqrt{(5)(3)}=2\sqrt{15}[/tex]
Answer: A = 4√5, B = 2√15Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
5x + 3y = 18
5x - 3y = 30
5x - y = 30
5x + y = 18
The equation of line CD in standard form is;
B: 5x - 3y = 30
Equation of a lineFormula for slope of line between two coordinates is;
m = (y2 - y1)/(x2 - x1)
Thus, slope of line CD is;
m = (0 - (-5))/(6 - 3)
m = 5/3
Now, equation of a line in slope intercept form is; y = mx + cc is y - intercept which is when x = 0.
Point D gives us the x-intercept because y is zero.
Thus;
0 = (5/3)(6) + c
c = -10
Thus, the equation of the line CD is;
y = (5/3)x - 10
Multiply through by 3 to get;
3y = 5x - 30
>> 5x - 3y = 30
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The square of the sum of a number and 9 is ??????
[tex]n-a\ number\\\\(n+9)^2=n^2+2(n)(9)+9^2=n^2+18n+81\\\\Used\ (a+b)^2=a^2+2ab+b^2[/tex]
Answer:
(x+9)²
Step-by-step explanation:
The square of the sum of a number and 9 is in terms of x, is (x+9)²
Select the two pairs of figures are similar
Answer:
1st and last group represent similar figures.
Step-by-step explanation:
We have been given a graph. We are asked to find the similar figures.
We can see that triangles in the 1st group are similar triangles as the measure of their corresponding angles are equal.
We can see that rectangle in the last group are also similar as the sides of the yellow rectangle is 2 times the sides of smaller rectangle, therefore, last pair is also similar.
Therefore, 1st and last group represent similar figures.
keith and michelle went out to dinner. the total cost of the meal,including the tip,came to $53.70. if the combined tip came out yo 9.60,and each friend spent and equal amouny,how much did each friend pay not including the tip?
Answer:
23.45
5
Step-by-step explanation:
53.70-9.60 is 46.90
46.90 divided by 2 is 23.45
Each friend paid $22.05 before the tip.
Keith and Michelle's dinner bill is a mathematics problem that can be solved by subtracting the tip from the total bill to find the cost of the meal alone and then dividing that amount by two to find out how much each friend has to pay without the tip.
First, we subtract the combined tip of $9.60 from the total cost of the meal, which was $53.70. This gives us the cost of the meal before the tip was added:
$53.70 - $9.60 = $44.10
Next, since Keith and Michelle spent an equal amount, we divide the cost of the meal by 2 to find out how much each friend pays:
$44.10 / 2 = $22.05
So, each friend paid $22.05 for the meal before adding in the tip.
Nathan has two parents, four grandparents, and so on. Explain how you can write both an explicit formula and a recursive formula that represents the number of ancestors Nathan has if we go back n generations.
Answer:
Explicit formula
f(n) = 2*2⁽ⁿ⁻¹⁾
Recursive formula
f(n) = aₙ₋₁ * r
Step-by-step explanation:
Since, Nathan has two parents, four grandparents, and so on, it would form a Geometric Progression (GP) series for the number of Nathan's ancestors as below:-
2, 4, 8, 16, 32, ....
First term (a₁) = 2
Common Ratio (r) = [tex]\frac{a_{2} }{a_1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
So,
Number of ancestors of Nathan if we go back n generations = a₁r⁽ⁿ⁻¹⁾
Plugging in the values of a₁ and r, we get
f(n) = 2*2⁽ⁿ⁻¹⁾ [Explicit formula]
Now,
A geometric progression (GP) series is of the form,
a, ar, ar², ar³, ar⁴, ar⁵........
in which the first term a₁=a and other the terms are obtained by multiplying with r.
Observe that each term is r times the previous term. So, to get the [tex]n_{th}[/tex] term, we multiply [tex](n-1)_{th}[/tex] term by r.
i.e. aₙ = aₙ₋₁ * r
=> f(n) = aₙ₋₁ * r [Recursive formula]
which graph has a coefficient correlation r closeest to -0.95
Answer:
Graph has a coefficient correlation r closest to -0.95 is the b).
Step-by-step explanation:
The correlation refers to the slope of a function and the sign indicates the direction to be linear the correlation informs us that it is inversely proportional
Taking some number to realice
Y axis maximum 5
X axis maximum 5
Notice 5 is where cut axis y so b=5
Equation:
[tex]y=mx+b\\y=-0.95x + 5[/tex]
Replacing:
x1=1.25; x2=2.5; x3=3.8;
So:
(1.25, 3.8); (2.5, 2.625); (3.8, 1.39)
20% of miran’s allowance is 5$ how much is his total allowance?
Question
20% of miran’s allowance is 5$ how much is his total allowance?
Answer:
25 $
Step-by-step explanation:
you can solve with an equation
20 : 5 = 100 : x
x = 5 * 100 : 20
x = 25
or you can solve with an expression
5 : 20 * 100 =
25
-------------------------------
check
25 * 20% = 5
the answer is good
The U.S. has about 190 million acres of national forest. One square mile is the same as 640 acres. How many states the size of Wyoming will cover the same area as all the national forests in the U.S.? Wyoming is shaped much like a rectangle. It is about 352 miles long and 278 miles wide:
Answer:
Around 3
Step-by-step explanation:
It is given that 1 sq. mile is equal to 640 acres.
Let's convert 190 million acres to sq. miles.
[tex]190,000,000*\frac{1Sq.Mi.}{640Acres}=296,875Sq.Mi.[/tex]
Taking Wyoming as a rectangle, we can find the area of Wyoming by multiplying length (352 miles) with width (278 miles).
Area of Wyoming is [tex]352*278=97,856[/tex]
To find the number of Whyoming's in total area of national forests, we divide the area of national forests (in sq. mi.) by the area of Wyoming ( in sq. mi.):
[tex]\frac{296,875}{97,856}=3.03[/tex]
So, around 3 Wyoming states' area will cover the area of national forests in US.
What’s the rate of change described in the table
Rate of change:
Answer:
(x+4,y+5)
Step-by-step explanation:
If you look at the differences in the x and y rows t=you can see that x is added 4 each time and y is add 5 each time.
please help immediately
Answer:
Look Below
Step-by-step explanation:
I'm not going to do any of these, i'll just set up the equation for you to find x.
9. 75+x=90
10. x+22=180
11. x=84
12. 82+78+x=180
13. (4x+3)+(x-8)=90
14. (8x+9)+(5x+15)=180 (This was hard to read, check to see if I typed it right.)
15. 2x+4+140=180
16. 4x-13=67+2x
17. 9x+7=115
18. 12x=60
19. 4x=x+21
20. 5x+12+73=180
Can someone please help me??
You didn't specify which problems you needed and you are only allowed to submit three questions in one posting so I chose to solve 1, 3, and 5.
NOTES:
Inverse means to swap the x's and y's and solve for "y"
*********************************************************************
1. Answer: y = [tex]\frac{2x+4}{3}[/tex]
Step-by-step explanation:
y = [tex]\frac{-4+3x}{2}[/tex]
swap: x = [tex]\frac{-4+3y}{2}[/tex]
2x = -4 + 3y
2x + 4 = 3y
[tex]\frac{2x+4}{3}[/tex] = y
3. Answer: y = -3(x - 1)
Step-by-step explanation:
y = [tex]-\frac{1}{3}x[/tex] + 1
swap: x = [tex]-\frac{1}{3}y[/tex] + 1
x - 1 = [tex]-\frac{1}{3}y[/tex]
-3(x - 1) = y
5. Answer: y = [tex]-\frac{4}{9}[/tex](x - 4)
Step-by-step explanation:
y = 4 - [tex]\frac{9}{4}x[/tex]
swap: x = 4 - [tex]\frac{9}{4}y[/tex]
x - 4 = [tex]-\frac{9}{4}y[/tex]
[tex]-\frac{4}{9}[/tex](x - 4) = y
10p - (3p - 4) = 4(p + 1) + 9
Answer:
p = 3
Step-by-step explanation:
distribute parenthesis on both sides of the equation
10p - 3p + 4 = 4p + 4 + 9 ( simplify both sides )
7p + 4 = 4p + 13 ( subtract 4p from both sides )
3p + 4 = 13 ( subtract 4 from both sides )
3p = 9 ( divide both sides by 3 )
p = 3
Write the arithmetic sequence 17,20,23,26... in standard form
Answer:
an=3n+14
Step-by-step explanation:
Use the formula
an=a1+d(n−1) to identify the arithmetic sequence.
an=3n+14
The standard form of the
Explanation:An arithmetic sequence is formed by adding a constant value to each term. In this case, the first term is 17 and the common difference is 3 (since we add 3 to each term to get the next term).
The standard form of an arithmetic sequence is:
an = a1 + (n-1)d
Where:
an represents the n-th term of the sequencea1 represents the first term of the sequenced represents the common differenceLet's calculate the standard form for the given arithmetic sequence:
an = 17 + (n-1)3
So, the standard form of the arithmetic sequence 17, 20, 23, 26... is an = 17 + 3(n-1).
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Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
The area of the section she wants to paint is 48 square feet.
In Euclidean Geometry, the area of a rectangle can be calculated by using this formula;
Area of rectangle = length × width
Area of rectangle 1 = 4 × 9
Area of rectangle 1 = 36 square feet.
For the area of rectangle 2, we have;
Area of rectangle 2 = 4 × 3
Area of rectangle 2 = 12 square feet.
Now, we can find the area of the figure;
Area of figure = 36 + 12
Area of figure = 48 square feet.
Complete Question:
Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
x/2+3=-5
solve step by step
Answer:
x=-16
Step-by-step explanation:
x/2+3=-5
Subtract 3 from each side
x/2+3-3=-5-3
x/2 = -8
Multiply each side by 2
x/2*2 = -8*2
x = -16
On average a cow produces 7 gallons of milk per day on average how many cups of milk will a cow produce in a week
i need help, i dont like math
Answer:
#1 is -1
Step-by-step explanation:
The answer to Problem 1 is the number -1. You use PEMDAS to evaluate division first, then you subtract later.
For problem 2, we combine like terms to get this answer: -4a+b. You only add the 'a' terms together, same with the 'b' terms. Think of it like having 2 books and add on 3 more books. We can write that as 2b+3b = 5b. So we have 5 books total.
Problem 3) The answer here is 1.2n after adding n to 0.2n. Think of the first n as 1n or 1.0n
Problem 4) Divide both sides by 15 and you end up with the answer a = 2
Problem 5) Answer: 31.4 This answer is found by multiplying the diameter (10) by the approximate value for pi (3.14). The formula is C = pi*d
John is twice as old as Bill. Greg is 7 years older than Bill. Four years ago, the sum of their ages was 55. How old is Greg?
Answer:
Greg is 67 years old.
Step-by-step explanation:
John = 2 * B
G = 7 + B
J - 4 + B - 4 + G - 4 = 55
J + B + G = 67
2B + B + 7 + B = 67
4B = 60
B = 15
J = 30
G = 22
30 + 15 + 22 = 67
67 = 67
- I.A -
The age of Greg is 31 years.
What is a linear equation?A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c.When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
Calculation:-
⇒let the actual age of Bill is X years.
four years ago the age Bill = X-4
⇒ then, the age of John is twice of Bill = 2X
four years ago age John = 2X-4
⇒Greg is 7 years older than Bill
Age of Greg = 2X+7
four years ago age Gerg = 2X+7-4
Four years ago Sum of their ages = 55
⇒ ( X-4)+(2X-4)+(2X+7-4)=55
⇒X-4+2x-4+2x+7-4=55
⇒5X=60
⇒X=12
∴age of Gerg is 2X+7
⇒2(12)+7
⇒31 years
age of bill=12 years
age of John 24 years.
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2. A forest preserve rents canoes for $18 per hour. Corey has $90 to spend. Write and solve an equation to find how many hours he can rent a canoe
Answer:
5 hours
Step-by-step explanation:
Let x be the number of hours.
18x=90
Divide by 18 on each side
x=5
Final answer:
Corey can rent the canoe for 5 hours with his $90 by setting up and solving the linear equation 18x = 90.
Explanation:
To determine how many hours Corey can rent a canoe, given that he has $90 to spend and the rental cost is $18 per hour, we can set up a linear equation. We let x represent the number of hours Corey can rent the canoe for.
The equation is simply 18x = 90, where 18 represents the hourly rental rate of the canoe and 90 represents the total amount Corey has to spend.
To solve for x, we divide both sides of the equation by 18:
18x / 18 = 90 / 18
x = 5
So, Corey can rent the canoe for 5 hours with his $90.
How can you decide which variable to solve for the first when you are solving a linear system by substitution
Answer:
The variable having largest coefficient is solved first.
Step-by-step explanation:
The variable having greater coefficient is solved first because we can substitute the value of smaller coefficient variable easily as compared to the greater one.
Because in substitution method we first substitute the value of coefficient which has smallest coefficient and as a result the coefficient with greater coefficient is solved.
Final answer:
When solving a linear system by substitution, choose the variable that is already isolated in one of the equations. Substitute the value of that variable into the other equation.
Explanation:
When solving a linear system by substitution, it is important to decide which variable to solve for first. One strategy is to choose the variable that is already isolated in one of the equations. This makes it easier to substitute the value of that variable into the other equation.
For example, consider the system:
Equation 1: x + 2y = 5
Equation 2: 3x - y = 2
In this case, Equation 1 is already isolated for x, so it would be a good choice to solve for x first. By substituting the expression for x from Equation 1 into Equation 2, you can solve for the remaining variable y. Once you have the value of y, you can substitute it back into Equation 1 to find the value of x.
The length of the base and the height of a triangle are numerically equal. Their sum is 6 less than the number of units in the area of the triangle. Find the area of the triangle.
Which ordered pairs are on the line 3x−4y=9 ?
Select each correct answer.
(1,−32)
(−1,3)
(−5,−6)
(23,−74)
Answer:
The ordered pair that is on the line is (−5,−6)
Step-by-step explanation: You have to substitute...
Soooo....
(1,-32):
3x − 4y = 9
3(1) - 4(-32) = 9
3 + 128 = 9
131 = 9
NO
Remember, a negative times a negative becomes positive.(-1,3):
3x − 4y = 9
3(-1) - 4(3) = 9
-3 - 12 = 9
-15 = 9
NO
Remember, a negative times a positive becomes a negative.Remember, a negative plus a negative becomes a negative.(-5, -6)
3x − 4y = 9
3(-5) - 4(-6) = 9
-15 + 24 = 9
9 = 9
YES
(23, -74)
3x − 4y = 9
3(23) - 4(-74) = 9
69 + 296 = 9
365 = 9
NO
By substituting the x and y values from the given ordered pairs into the equation, we find that the only ordered pair on the line represented by the equation 3x−4y=9 is (-5,-6).
Explanation:The equation 3x−4y=9 represents a line on a coordinate plane, and ordered pairs (x, y) are points on this plane. To determine which given ordered pairs are on the line, we substitute each x and y value into the equation.
For (1,-32), the equation becomes: 3*1 - 4*(-32) = 9. This simplifies to 3 + 128, which does not equal 9, therefore (1,-32) is not on the line. For (-1,3), the equation becomes: 3*(-1) - 4*3 = 9. This simplifies to -3 - 12, which also does not equal 9, therefore (-1,3) is not on the line. For (-5,-6), the equation becomes: 3*(-5) - 4*(-6) = 9. This simplifies to -15 + 24, which equals 9. So, the ordered pair (-5,-6) is on the line. For (23,-74), the equation becomes: 3*23 - 4*(-74) = 9. This simplifies to 69 + 296, which does not equal 9, therefore (23,-74) is not on the line.
The only correct ordered pair on the line 3x−4y=9 is (-5,-6).
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Simplify the expression by combining like terms. 23+6c+8d−7d−6
Answer:
17 + 6c +d
Step-by-step explanation:
To simplify the expression, we need to combine like terms
23+6c+8d−7d−6
I like to put like terms next to each other
23-6+6c+8d−7d
17 + 6c +d
23 + 6c + 8d - 7d - 6
combine like terms
= 6c + (8d - 7d) +(23 - 6)
= 6c + d + 17Forrest Lumber purchased a table saw for $735. After 2 years the saw had a depreciated value of $525. What is the amount of yearly depreciation? A. $105 B. $210 C. $90 D. $120
Final answer:
The amount of yearly depreciation for the table saw is calculated by subtracting the depreciated value from the original cost and dividing by the number of years, resulting in an amount of $105 per year.
Explanation:
The question involves calculating yearly depreciation of an asset, which is a common topic in accounting and finance sections of high school mathematics or business studies.
To find the amount of yearly depreciation, we subtract the end value of the asset after depreciation from its original cost and then divide by the number of years over which the depreciation occurred. In this case, we have:
Original cost of the saw = $735
Depreciated value after 2 years = $525
Depreciation over 2 years = Original cost - Depreciated value
Depreciation over 2 years = $735 - $525 = $210
Yearly depreciation = Depreciation over 2 years ÷ Number of years
Yearly depreciation = $210 ÷ 2 = $105
Therefore, the yearly depreciation of the table saw is $105, which corresponds to option A.
At lunch, $60\%$ of the students selected soda while $20\%$ selected milk. If 72 students selected soda, how many students selected milk?
Answer:
24 students
Step-by-step explanation:
If 60% equals 72, then 20% would be 1/3 of 72 which is 24.
Answer:
24 students selected milk
Step-by-step explanation:
Let x be the total number of students,
Since, 60% of students selected soda,
⇒ Number of students who selected soda = 60% of x = 0.6x
According to the question,
0.6x = 72
Divide both sides by 0.6,
⇒ x = 120
Now, 20% students selected milk
Hence, the number of student who selected milk = 20% of 120 = 0.20 × 120 = 24
2/3 + 5/6
Explain how to do it
Answer:
It's simple Add the fractions, find the LCD and then combine
Exact form: 3/2
Decimal form: 1.5 Hope this helps have a nice day :)
Step-by-step explanation:
Answer:
4/6 + 5/6 = 9/6
Step-by-step explanation:
First find the least common denominator which is 6. Then add the fractions. Hope this helps.
to the nearest tenth, what is the length in units of MN?
Answer:
10
Step-by-step explanation:
Answer:
b) 6.7
Step-by-step explanation:
Point M has the coordinates (2, -3)
Point N has the coordinates (8, -6)
The length of the segment MN is computed as follows:
L =√[ (xN - xM)² + (yN - yM)² ]
L =√[ (8 - 2)² + (-6 - (-3))² ]
L =√[ 36 + 9 ]
L = 6.7