Answer:
H0: μ ≤ 68,800
H1: μ > 68,800
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (H1) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
The Null hypothesis is that the average attendance at games is less than or equal to 68,800.
H0: μ ≤ 68,800
The alternative hypothesis is that the average attendance at games is over 68,800.
H1: μ > 68,800
H₀: μ ≤ 68,800 H₁: μ > 68,800. Then the correct option is D.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomenons under the assumption, or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
The Null hypothesis is that the average attendance at games is less than or equal to 68,800.
H₀: μ ≤ 68,800
The alternative hypothesis is that the average attendance at games is over 68,800.
H₁: μ > 68,800
Then the correct option is D.
More about the null hypotheses and alternative hypotheses link is given below.
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Using tan(A+B), find the exact value of tan(105).
Answer:
-2-√3
Step-by-step explanation:
The sum of angles formula for tangent is ...
tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))
For the desired angle, we can use A=45°, B=60°. Then we have ...
tan(105°) = (tan(45°) +tan(60°))/(1 -tan(45°)tan(60°))
The tangent values we need are ...
tan(45°) = 1
tan(60°) = √3
Then our tangent is ...
tan(105°) = (1 +√3)/(1 -1·√3) = (1 +√3)²/((1 -√3)(1 +√3)) = (4+2√3)/(-2)
tan(105°) = -(2+√3)
A firm produces two types of earphones per year: x thousand of type A and y thousand of type B. The cost function (in thousands of dollars) is given by
C(x,y)=110+80x+130y
If the selling price of type A is p and the selling price of type B is q, the price-demand equations are
p=120-3x+y
q=210+x-7y
Determine how many of each type of earphone should be produced per year to maximize profit? What should be the selling prices p and q? What is the maximum profit?
Answer:
9000 A and 7000 B should be producedp = 100, q = 170$350,000 is the maximum profitStep-by-step explanation:
We assume that "p" and "q" are given in dollars, so that the profit function (in thousands of dollars) can be written:
P = xp +yq -C(x, y)
Profit will be maximized when the partial derivatives of P with respect to x and y are both zero:
∂P/∂x = p +x(∂p/∂x) +y(∂q/∂x) -∂C/∂x = 0
(120 -3x +y) +x(-3) +y(1) -80 = 0
-6x +2y +40 = 0
3x -y = 20 . . . . put in standard form
and ...
∂P/∂y = x(∂p/∂y) +q +y(∂q/∂y) -∂C/∂y = 0
x(1) +(210 +x -7y) +y(-7) -(130) = 0
2x -14y +80 = 0
x -7y = -40 . . . . put in standard form
__
The solution to these simultaneous equations can be found a variety of ways. Using Cramer's Rule, we have ...
x = ((-1)(-40) -(-7)(20))/(-1·1-(-7)(3)) = 180/20 = 9
y = (20(1) -(-40)(3))/20 = 140/20 = 7
9000 type A and 7000 type B earphones should be produced.
__
The corresponding selling prices are ...
p = 120 -3(9) +7 = 100
q = 210 +9 -7(7) = 170
The selling prices should be ...
p = $100, q = $170
__
The maximum profit is ...
P = xp +yq -C(x, y) = (9)(100) +(7)(170) -(110 +80(9) +130(7))
P = 9(100 -180) +7(170 -130) -110 = 180 +280 -110
P = 350
The maximum profit is $350,000.
Alice and Bob share some money in the
ratio 7:5. Alice got £4 more than Bob. How
much did Alice get?
Answer:
14
Step-by-step explanation:
7-5 = 2
4/2 = 2
2 x 7 = 14
After flooding damaged much of the crop, the cost of a head of lettuce jumped from $0.92 to $2.26. What percent of increase is this? Round to the nearest one percent.
Answer:
146%
Step-by-step explanation:
[tex] percent~change = \dfrac{new~price - old~price}{old~price} \times 100% [/tex]
If the percent change is positive, it is a percent increase.
If the percent change is negative, it is a percent decrease.
Your numbers are
old price = $0.92
new price = $2.26
Plug in the numbers in the formula above and evaluate the expression.
percent change = ($2.26 - $0.92)/($0.92) * 100%
percent change = ($1.34)/($0.92) * 100%
percent change = 1.4565 * 100%
percent change = 146%
Since the percent change is a positive number, it is a percent increase.
Answer: The percent increase is 146%.
f(x)=7x+3 and g(x)=-6x-8, find (f•g)(x) and (f•g)(-1)
Answer:
[tex](f*g)(x)=-42x^2-74x-24[/tex]
[tex](f*g)(-1)=8[/tex]
Step-by-step explanation:
[tex]f(x)=7x+3\\ g(x)=-6x-8[/tex]
[tex](f*g)(x)=(7x+3)(-6x-8)\\(f*g)(x)=-42x^2-56x-18x-24\\(f*g)(x)=-42x^2-74x-24[/tex]
Now;
[tex](f*g)(-1)=-42x^2-74x-24\\(f*g)(-1)=-42(-1)^2-74(-1)-24\\(f*g)(-1)=-42(1)+74-24\\(f*g)(-1)=-42+50\\(f*g)(-1)=8[/tex]
A tennis ball machine shoots 21 forehands 25 backhands and 9 lobs if a player missed 6 forehands 17 backhands and 2 lobs how many balls were hit
Answer:
30
Step-by-step explanation:
55 - 25 = 30
Solve: 3x
+ 4 = 5x - 4x - 8
Answer:
3x = - 18
Step-by-step explanation:
1. Simplify this equation in terms of what is already provided:
3x + 4 = 5x - 4x - 8 ⇒ 3x + 4 = x - 8
2. Now subtract 3x from either side, at the same time adding 8 to either side: 3x + 4 = x - 8 ⇒ 4 = -2x - 8 ⇒ 12 = -2x
3. Divide -2 on either side to isolate the x, and recieve it's value:
12 = -2x ⇒ x = 12/-2 ⇒ x = -6
4. The question demads for the value of 3x, so simply multiply the known value of x by 3, as such: x = -6 ⇒ 3x = -6 * 3 = -18
what are three segments from this figure?
Answer:
AD, DA, ED, DE
Step-by-step explanation:
Describe how to graph point K at (5, 4) the steps
Answer:
here is ur answer
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answer:
Step-by-step explanation:
B or c
Peter rolls a fair dice 114 times. How many times would Peter expect to roll a number greater than 1?
Answer:
A dice of six faces has 5 numbers bigger than 1 (from 2 to 6).
Then, the number Peter is expecting is : 114 x (5/6) = 95 (times)
Hope this helps!
:)
what is the area of a circle with the equation (x − 6)² + (y + 2)² = 17 ?
Answer:
17π
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
Area of a circle is:
A = πr²
r² = 17, so A = 17π.
Jonas is buying a three-day supply of camping snacks. An energy bar costs $1.50, and a bag of dried
mangoes costs $3.00. Jonas plans to have 7 snacks per day and can spend up to $45.00.
If p is the number of energy bars he can buy, and m is the number of bags of mangoes he can buy,
which system of equations and inequalities can be used to represent the possible number of each
snack he can buy?
p+m
21
=
21
p+m = 45
1.5p + 3m
p> 0
m >0
1.5p + 3m < 45
p> 0
m 2 0
1.5p + 3m
3p + 1.5m
p20
m 20
p+m = 21
8p + 1.5m
p> 0
m >0
Answer:
P+m=21
1.5p + 3m < 45
p > 0
m > 0
Step-by-step explanation:
A shoe manufacturer was investigating the weights of men's soccer cleats. He felt that the weight of these cleats was less than the average weight of 10 ounces. After a random sample of 13 pairs of cleats, he found that sample mean was 9.63 and the standard deviation was .585. At a significance level of .05, can it be concluded that the researcher was correct?
Show work
Answer:
The conclusion is that the researcher was correct
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 13[/tex]
The sample mean is [tex]\= x = 9.63[/tex]
The standard deviation is [tex]s = 0.585[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is [tex]H_o : \mu = 0[/tex]
The Alternative Hypothesis is [tex]H_a = \mu < 10[/tex]
The test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]
Substituting values
[tex]t = \frac{9.63 - 10 }{\frac{0.585}{\sqrt{13} } }[/tex]
[tex]t = - 2.280[/tex]
Now the critical value for [tex]\alpha[/tex] is
[tex]t_{\alpha } = 1.645[/tex]
This obtained from the critical value table
So comparing the critical value of alpha and the test value we see that the test value is less than the critical value so the Null Hypothesis is rejected
The conclusion is that the researcher was correct
the price increase of a set of golf clubs is from $250 to $750. What is the percent increase?
Answer:
300%
Step-by-step explanation:
3 times 250 is 750
subtract 6066 from 294
Answer:
-5772
Step-by-step explanation:
294-6066=-5772
Answer:
The answer would be 2,772
Step-by-step explanation:
6,066 - 294 = 2,272
I hope that helps!!:)
Every year, census researchers collect data from 850 public and private hospitals across the United States. Which issue will invalidate the conclusion of the hypothesis test? Group of answer choices The data comes from only 850 hospitals in the U.S. when there are 5,700 hospitals in the U.S. Researchers received more data from public hospitals than from private hospitals. The data is selected by choosing the first 850 hospitals from an alphabetized list.
Answer:
Option C
Step-by-step explanation:
For a better, clear and unbiased sampling, choosing randomly might not allow for a biased sampling. Choosing in an alphabetical order might not give a representative of the whole hospitals both private and public, thus invigilator the conclusion of our hypothesis test.
£48 is divided between Alf and Ted in the ratio of 7:9. How much does Alf receive?
7:9=7+9=16
Alf is 7 which means 7/16*£48=6.125
Giving brainliest for CORRECT awnser.
Answer:
B.
Step-by-step explanation:
So, first off, the quadratic formula is -b plus or minus sqrt(b^2-4ac)/2a. Plug the equation given, and you get B.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply
A sculpture sits on a pedestal in the shape of a square prism. The side lengths of a base of the prism are 3 feet. The height of the prism is 4 feet. The museum director wants to cover all but the underside of the pedestal with foil that costs $0.22 per square foot. How much will the foil cost?
Answer:
Total cost of covering the pedestal is $12.54.
Step-by-step explanation:
The pedestal is a square prism so top and bottom are of square shape.
Hence, we have here length = width
We know that the Total Surface Area of a Prism is:
[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]
Where l is length,
w is width and
h is height of prism
We know that here w = l = 3 feet
and h = 4 feet
Also, underside of pedestal is not to be covered.
The underside of pedestal is square type.
So,
[tex]\text{Required Total Surface Area = } l\times w+ 2\times w \times h+2\times h \times l[/tex]
[tex]\Rightarrow 3 \times 3 + 2 \times 3 \times 4 + 2 \times 3 \times 4\\\Rightarrow 9 + 24 + 24\\\Rightarrow 57\ ft^{2}[/tex]
Cost of cover per square foot = $ 0.22
Total cost of [tex]57\ ft^{2}[/tex] [tex]\Rightarrow 0.22 \times 0.57 = \$12.54[/tex]
Find the sum of the interior angle measures of a convex octagon (an eight-sided polygon).
Answer:
1080
Step-by-step explanation:
:)
(-3x + 15) + (-3x + 2)
Answer:
If you are looking for a simplified equation, then the answer is -6x + 17
Step-by-step explanation:
(-3x + 15) + (-3x + 2)
Because you are only adding and subtracting here, you can take out the parentheses.
-3x + 15 -3x + 2
= -6x + 17
Please help ASAP! I will mark Brainliest! Please READ the question THEN answer CORRECTLY! No guessing!
Answer:
its C
Step-by-step explanation:
Hope this helps!!
Answer:
B. Week 6
Step-by-step explanation:
[tex]f(x) = 2^{x}[/tex]
We know that f(x) represents number of subscribers, x represents week number. So plug in 64 for f(x).
[tex]64 = 2^{x}[/tex]
Uh-oh, how do we solve this? We need to go from exponential form to logarithmic form.
[tex]64 = 2^{x}[/tex]
log₂(64) = x
We're basically asking the question: 2 to the what equals 64? And we can plug this into the calculator as log₂(64) (on TI-84, it's MATH->logBASE(). Or you can just think about it:
2 x 2 x 2 x 2 x 2 x 2 = 64.
There are 6 2s, so 6 is the answer.
Today a shoe store it’s at 20% of the price of a pair shoes and for the next three days it will take 20% of the previous days price if the price of a pair of shoes yesterday was $200 what will be the price of the pair of shoes three days from now
A.160.00
B.128.00
C.102.40
D.81.92
If the price of the shoe yesterday was $200 and on this day 20 percent has been taken thus it will have $160. In the next 3 days if another 20 percent will be taken out from the previous $160 then the final answer is $128.
ps.. can u give brainly pls :3
A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes. The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts. What is the probability of randomly selecting an item with white or red on it?
A) 1/4 B) 3/10 C)1/2 D) 7/10
Answer:
its 7/10
Step-by-step explanation:
The probability of randomly selecting an item with white or red on it is 3/10.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes.
The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts.
The probability of randomly selecting an item with white or red on it is given by;
[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\[/tex]
Total items = 2 + 1 + 3 + 2 + 1 + 1 = 10 itens.
Substitute all the values in the formula
[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\\\\rm Probability=\dfrac{3}{10}\\\\[/tex]
Hence, the probability of randomly selecting an item with white or red on it is 3/10.
Learn more about probability here;
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HELP ME PLEASE , ALOT OF POINTS, CHECK DOCUMENT! Show work
Answer:
x=8
Step-by-step explanation:
log4( x-6) +log4(x) = 2
We know that loga + log b = log (ab)
log4( x-6)(x) = 2
Raise each side to the base of 4
4^log4( x-6)(x) = 4^2
( x-6)(x) = 16
Distribute
x^2 -6x = 16
Subtract 16 from each side
x^2 -6x-16 = 0
Factor
(x-8) (x+2) =0
Using the zero product property
x-8=0 x+2 =0
x=8 x=-2
Checking, we cannot have the log of a negative number so -2 is not a solution
Answer:
x = 8
Step-by-step explanation:
log4(x - 6) + log4(x) = 2
log4[(x - 6) × x] = 2
x² - 6x = 4²
x² - 6x - 16 = 0
x² - 8x + 2x - 16 = 0
x(x - 8) + 2(x - 8) = 0
(x + 2)(x - 8) = 0
x = 8, -2
Log of negative numbers do not exist, so x is only 8
In the diagram below, point P is circumscribed about quadrilateral ABCD. What is the value of x? (Pls answer I give lot of point)
Answer:
D. 50
Step-by-step explanation:
130+x=180
x=50
What is 4/12 x 70.please help me
Answer:
70/3
Step-by-step explanation:
Your welcome :)
Step-by-step explanation:
4 / 12 = 1/3 = 0.33
0.33 x 70 = 23. 33
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:D
Step-by-step explanation:
(4/5)^0
(4^0)/(5^0)=1/1=1
