Answer:
The conclusion
There is sufficient evidence to conclude that the the residents of this particular city are spending significantly (at 5% level) more time watching TV than the average for this geographic area.
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 13 \ hours\ per\ week[/tex]
The sample size is n= 16
The sample mean is [tex]\= x = 15.3[/tex]
The standard deviation is [tex]s = 3.8\ hours.[/tex]
The null hypothesis is [tex]H_o : \mu = 13[/tex]
The alternative hypothesis is [tex]H_a : \mu > 13[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{15.3 - 13 }{ \frac{ 3.8 }{\sqrt{16} } }[/tex]
=> [tex]t = 2.42[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(z > 2.42)[/tex]
From the z -table
[tex]P(z > 2.42) = 0.0077603[/tex]
=> [tex]p-value = 0.0077603[/tex]
From the values obtained we see that [tex]p-value < \alpha[/tex]
Hence we reject the null hypothesis
Therefore there is sufficient evidence to conclude that the the residents of this particular city are spending significantly (at 5% level) more time watching TV than the average for this geographic area.
Find the slope of the line joining the points (2, 5) and (3, 1)
Slope = change in Y / change in x
slope = (1-5) /(3-2)
Slope = -4/1
Slope = -4
Answer:
slope = -4
Step-by-step explanation:
The formula for finding slope is (y2 - y1)/(x2 - x1)
x1 = 2
y1 = 5
x2 = 3
y2 = 1
Plugging in our numbers,
(1 - 5)/(3 - 2) = -4/1
= -4
Find the value of the expression -20 / -4
Answer:
5
Step-by-step explanation:
-20 / -4 = 5
A negative divided by a negative is positive!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
The area of the triangle is 3 square miles.
h
2 mi.
What is the triangle's height, h?
Answer:
3 mi
Step-by-step explanation:
Use the equation for area of a triangle, A = 1/2 * base * height. Plug in the numbers you have and solve for the height, You get that 3 = 1/2 * 2 * h, and that h = 3.
Hopefully this helps- let me know if you have any questions!
please help me I am so lost on this question. thank you have a good blessing day
Answer: x=-3
Step-by-step explanation:
In this question, they simply want you to find a pair of x and y-coordinates that would be valid in this equation.
We can take a random number for x, like, say, 3.
y = 2x + 6
y = 2(3) + 6
y = 6 + 6
y = 12
Since giving the value of 3 to x results in y being 12, we can safely say that the coordinates (3, 12) would be valid in this equation. Therefore:
(12) = 2(3) + 6
Let me know if you need me to explain anything.
- Breezyツ
A company has been forced to reduce its number of employees. Today the company has 34% fewer employees than it did a year ago. If there are currently 297 employees, how many employees did the company have a year ago?
Write an equation of a line through (5,6) and perpendicular to the line through (4,8) and (-2,-18). please help, will mark brainliest. You also get 10 points
Answer:
y = 4 1/3x+ 6
Step-by-step explanation:
Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept. The y-intercept occurs at x=0 or point (0,b).
-18 -8 / -2 - 4 = -26 / -6 = 4 1/3 perp = - 4 1/3 = y=4 1/3 x+b
Step 2. -18 -8 / -2 - 4 = -26 / -6 = 4 1/3 perp = - 4 1/3 is a vertical line or parallel to the y-axis. So a line perpendicular to x= 4 1/3 is a horizontal line parallel to the x-axis.
Step 3. Therefore y= 4 1/3 is a horizontal line parallel to the x-axis. Now, the line needs to pass through point (5,6) or x=5 and y=6. Then, y=b=6 or y=6 is the equation of the line. but then x = 4 1/3 so y = 4 1/3x + 6
Step 4. ANSWER: The equation is y = 4 1/3x+ 6 where slope m=4 1/3 and y intercept b=6.
Triangle ABC is shown with its incenter at D. The inscribed circle's radius measures 2 units. The length of AB is 9 units. The length of BC is 10 units. The length of AC is 17 units.
What is the area of triangle ACD?
What is the area of triangle ABC?
The area of triangle ACD and ABC are 17 and 46.75 square units respectively
How to find the area of a triangleThe formula for finding the area of a triangle is expressed as:
A = 0.5bh
where:
b is the base
h is the height
Area of the triangle ACD = 0.5DE * AC
Area of the triangle ACD = 0.5(2)(17)
Area of the triangle ACD = 17 square units
For the triangle ABC
Area = 0.5(BE)(AC)
Area= 0.5(5.5)(17)
Area = 46.75square units
Hence the area of triangle ACD and ABC are 17 and 46.75 square units respeectively
Learn more on area of triangle here: https://brainly.com/question/17335144
Can someone help me with this please
Answer:
17 is the answer for #4
1. Write the equation for each of the following:
- Slope Intercept:
- Point-Slope:
- Standard Form:
6 cupcakes for £5 or 4 cupcakes for £3.50
Answer:
6 cupcakes for £5
Step-by-step explanation:
Given :-
Two options
6 cupcakes for £54 cupcakes for £3.50To Find :-
Which is better value for money
Solving :-
Find the cost of one cupcake of the two options
1. 6 cupcakes = £5
=> 1 cupcake = £0.83
2. 4 cupcakes = £3.50
=> 1 cupcake = £0.875
Solution :-
It would be wiser to purchase 6 cupcakes for £5
1/3=7/21, .. What are the means
Answer:
Equivelant fractions.
Step-by-step explanation:
Ask your self..
How did the 1/3 become 7/21?
Its very simple multiply 1/3's numerator and denominator by 7
So its going to be.. 1 x 7 = 7
3 x 7 = 21
Therefore, we have 7/21
PLEASE HELP!!!!!TIMED!!!!!! 21 MINS LEFT!!!! 30 POINTS!!!!!!!Which is the last operation performed when evaluating (8 - 2) * 4 for x=3
Answer:
Multiplication.
Parentheses comes first, regardless of PEMDAS. When you see parentheses, only the P for parentheses in PEMDAS should be your main concern.
The amount of money spent at a gas station varies directly with the number of gallons purchased. When 15.5 gallons of gas was purchased , the cost was $48.67. What is the cost for 9 gallons of gas?
Answer:
$28.26
Step-by-step explanation:
In order to find out how much each gallon of gas cost, you need to divide the $48.67 by the 15.5 gallons. This would equal 3.14 So the cost for one gallon is $3.14
Then you would need to multiply this number by the 9 gallons to get the price. Which would equal $28.26
20% of what number is = to 5% of 680
Answer:
Solution
20%× X= 5%×680
or, X=170.
The required number is 170.
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If not possible, enter IMPOSSIBLE.) A = 72°, a = 34, b = 21
Answer:
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Step-by-step explanation:
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin B}{21} [/tex]
[tex] \sin B = \dfrac{21\sin 72^\circ}{34} [/tex]
[tex] \sin B = 0.5874 [/tex]
[tex] B = \sin^{-1} 0.5874 [/tex]
[tex] B = 35.97^\circ [/tex]
C = 180° - 72° - 35.97°
C = 72.03°
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin 72.03^\circ}{c} [/tex]
[tex]c = \dfrac{\sin 72.03^\circ \times 34}{\sin 72^\circ}[/tex]
[tex] c = 34.00 [/tex]
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Answer:
[tex]B\approx35.97^\circ\\C\approx72.03^\circ\\c\approx34[/tex]
Step-by-step explanation:
Law of Sines
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
Given information
[tex]A=72^\circ\\a=34\\b=21[/tex]
Check if solutions exist
As [tex]A=72^\circ < 90^\circ[/tex] and that [tex]a > b\rightarrow 34 > 21[/tex], then there exists only one possible triangle by the Ambiguous Case
Solve the triangle
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(B)}{21}\\ \\ 21sin(72^\circ)=34sin(B)\\\\\frac{21sin(72^\circ)}{34}=sin(B)\\ \\B=sin^{-1}(\frac{21sin(72^\circ)}{34})\\ \\B=35.97394255^\circ\approx35.97^\circ[/tex]
[tex]A+B+C=180^\circ\\\\72^\circ+35.97394255^\circ+C=180^\circ\\\\107.97394255^\circ+C=180^\circ\\\\C=72.02605745^\circ\approx72.03^\circ[/tex]
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(72.02605745^\circ)}{c}\\\\c*sin(72^\circ)=34sin(72.02605745^\circ)\\\\c=\frac{34sin(72.02605745^\circ)}{sin(72^\circ)}\\ \\c=34.00502065\approx34[/tex]
Which of the following relations represent a function?
A. {(-1,-3),(3,2),(3,7)}
B.{(-1,4),(2,7),(3,7)}
C.{(-3,7),(3,-7),(3,7)}
D. {(-1,4),(-1,7),(3,5)}
100 POINTS
#A
(-1,3)(3,2)(3,7)3 has two images 2,7 hence not a function
#B
(-1,4)(2,7)(3,7)Every domain has unique range hence function
#C
(-3,7)(3,-7)(3,7)3 has two images hence not a function
#4
-1 has two images hence not a function
Shelley is going shopping before her vacation. Each outfit costs $20 and she wants to spend no more than $180. Write an inequality that represents the number of outfits, f, she can purchase without going over her $180 budget
Please help I'm failing math
HELP IS NEEDED ASAP! WILL MARK THE BRAINLIEST FOR THE CORRECT ANSWER, NOT SOME SPAM OF LETTERS.
Answer:
1. A: 1
2. B 2[tex]\pi[/tex]
Step-by-step explanation:
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day! :)
Don’t mind my handwriting but can someone help me please
Answer: A: 3/5
Step-by-step explanation:
He made 9 shots
He attempted 15
The ratio will be 9/15, which can be simplified to 3/5
Have a nice day :)
Answer:
A) 3/5
Step-by-step explanation:
No.of baskets attempted = 15
No.of baskets made = 9
Given, To find the ratio of no.of baskets made to no.of baskets attempted
Then,9:15 (or) 9/15
If we simplify 9/15, we get 3/5
THANKYOUPlease mark me as brainliest
What can be the last digit of a a square of a natural number?
Answer:
1, 4, 5, 6, & 9 are the only digits that can be the last digit of the square of a natural number.
Step-by-step explanation:
HELP ME PLSSSSSSSSSSSS
Answer:
7 cubic units
Step-by-step explanation:
There are 6 unit cubes on the bottom layer, and one on the top layer. The total volume is ...
6 +1 = 7 . . . . cubic units
NEED HELP ON HELP ON HOW TO DO THIS
You have triangle JKL. Angle J is a right triangle. Angle K has a measure of 40 degrees. Side k=26. Solve the triangle. Round angles and sides to nearest tenth.
Answer choices:
A) Angle L= 50 degrees, side L= 31.0, side J= 40.4
B) Angle L= 50 degrees, side L= 33.3, side J= 42.8
D) Angle L= 50 degrees, side L= 21.8, side J= 33.9
E) Angle L= 50 degrees, side L= 33.9, side J= 21.8
Pls give explanation!!
Answer:
Option E
Step by step explanation:
We know that angle J is a right angle meaning it's an angle 90 degrees. So to find angle L;
90+40+L=180
130+L=180
L=180-130
So therefore angle L =50 degrees
Now to find side J which is the opposite in the triangle,we use tan because it has adjacent and opposite which is what we're looking for;
Tan 40 degrees =opposite/26
We cross multiply
Opposite =Tan 40 degrees×26
Opposite =21.8
Side J=21.8
With side J found we can find side L using Pythagoras theorem
L^2=21.8^2 +26^2
L^2=475.24+676
L^2=1,151.24
L=Square root of 1,151.24
L=33.9
Answer:
A) Angle L= 50 degrees, side L= 31.0, side J= 40.4
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. The given side of k is opposite the given angle K, so the sine or tangent functions can be used to find missing sides. If we want to start with the hypotenuse, we can use the relation ...
Sin = Opposite/Hypotenuse
sin(40°) = 26/j
j = 26/sin(40°) ≈ 40.4 . . . units (matches choice A)
Similarly, we can use the tangent relation to find side ℓ:
Tan = Opposite/Adjacent
tan(40°) = 26/ℓ
ℓ = 26/tan(40°) ≈ 31.0 . . . units (matches choice A)
Of course, angle L is the complement of 40°:
L = 90° -40° = 50°
The solution to the triangle is L = 50°, ℓ = 31.0, j = 40.4.
Ali says that the perimeter of the rectangle on the coordinate plane is equal to 30 units , choose the correct answer that shows Ali's mistake ?
Answer:
perimeter =22units
Step-by-step explanation:
30units is supposed to be the are and its supposed to be 30 units squared
V= 11.43
L= 2.5
W= 1.2
Depth is 3.81
Step-by-step explanation:
V = l x w x d
11.43 = 2.5 x 1.2 x d
11.43 = 3 x d
÷3
3.81 = d
Hope this helps!
Solve this quadratic equation by completing the square
x^2=12x+17
Answer:
[tex]\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }[/tex]
Step-by-step explanation:
We would like to solve the given quadratic equation by completing the square method .The given equation is ;
[tex]\longrightarrow x^2=12x +17[/tex]
Subtract 12x to both sides ,
[tex]\longrightarrow x^2-12x = 17 [/tex]
Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,
[tex]\longrightarrow x^2-2(6)(x) = 17 [/tex]
Add 6² on both sides ,
[tex]\longrightarrow x^2-2(6)(x) + 6^2=17+6^2 [/tex]
Now LHS is in the form of (a-b)² = a²-2ab+b² ; so that ;
[tex]\longrightarrow (x -6)^2 = 17+36 [/tex]
Simplify RHS ,
[tex]\longrightarrow (x-6)^2=53 [/tex]
Put square root on both sides,
[tex]\longrightarrow (x-6) = \pm\sqrt{53}[/tex]
Add 6 on both sides,
[tex]\longrightarrow x = 6\pm\sqrt{53} [/tex]
Separate the two solutions ,
[tex]\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}} [/tex]
And we are done!
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high
temperature of 83 degrees occurs at 5 PM and the average temperature for the day is 65 degrees. Assuming
t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Answer:The temperature at 4 AM is 41 degrees.
Step-by-step explanation:
We have an average temperature of 45 degrees and a high of 53 degrees. That makes the midline 45 and the amplitude 8.
We could spend some time trying to figure out how to get a graph in which x=0 corresponds to midnight. However; that is not necessary. We can use any sinusoidal function we want, as long as we understand which part of the graph corresponds to what hour of the day.
So with midline 45 and amplitude 8, let's choose a simple function:
f%28x%29+=+45%2B8sin%28x%29
The time at which we are to find the temperature, 8 AM, is 8 hours before 4 PM, which is the time when the temperature is maximum. 8 hours is 1/3 of a day, so we want to find the temperature 1/3 of a cycle before 4 PM.
Since we are using a sine function with no horizontal shift, the time of maximum temperature, 4 PM, corresponds to 1/4 of the way through a cycle, at pi/2.
We want to go back 1/3 of a cycle, or (2/3)pi, from pi/2; that puts us at -pi/6.
That makes it easy to find the temperature at 4 AM without a calculator:
45%2B8%2Asin%28-pi%2F6%29+=+45%2B8%28-.5%29+=+45-4+=+41
The temperature at 4 AM is 41 degrees.
Answer:
probably he temperature at 4 AM is 41 degrees.
Step-by-step explanation:
The bank requires that the Dotkoms pay their homeowner's insurance, property taxes,
and mortgage in one monthly payment to the bank. If their monthly mortgage payment
is $1,711.22, their semi-annual property tax bill is $3,239, and their annual homeowner's
insurance bill is $980, how much do they pay the bank each month?
Using proportions, it is found that they pay the bank $2332.72 each month.
What is a proportion?A proportion is a fraction of a total amount.
Their payments are given by:
Monthly mortgage of $1,711.22.Semi-annual property tax bill is $3,239, that is, it is paid every 6 months, hence 3239/6 = $539.83.Annual insurnce of $980, hence 980/12 = $81.67 each month.Then, the total amount is:
1,711.22 + 539.83 + 81.67 = $2332.72.
More can be learned about proportions at https://brainly.com/question/24372153
Three times a number decreased by 9
Answer:
3x-9
Step-by-step explanation:
Answer:
does this help?........
Find the area of a rectangular park which is 183/5 m long and 50/3 m broad.
Answer:
Area of a triangle = l*b
= 183/5*50/3
= 36.6*16.66
= 609.756 m
Which is equal to 3 x 2-4
Answer:
2
Step-by-step explanation:
Answer:
the correct answer is 2
Step-by-step explanation:
hope you have a great day -TJ
may i pls have brainliest thank you