Answer:
Temperature after 1 minute = 184 ° F
Step-by-step explanation:
starting temperature = 200 °F
rate of decrease = 8% per minute
Temperature lost = 8% of 200 = 8/100 × 200 = 0.08 × 200 = 16 °F
It therefore means that after 1 minute, the cup of coffee loses 16 °F,
∴ Temperature after 1 minute = (starting temperature) - (lost temperature)
= 200 - 16 = 184 °F
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to fill the pool if the drain is left open?
Answer:
72
Step-by-step explanation:
A trapezoid has an area given by A =1-2(b1+b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.
Answer:
b1 = (28/h) -b2
Step-by-step explanation:
Filling in the given value for A, you have ...
14 = (1/2)(b1 +b2)h
Multiply by 2/h:
28/h = b1 +b2
Subtract b2:
b1 = (28/h) -b2
What is the value (hundredth) of the ratio of the circumference of a circle
to its diameter?
Answer:
3.14Step-by-step explanation:
the circumference of a circle = Diameter × π
in other words ,the ratio of the circumference of a circle to its diameter is π
and we know that π = 3.14159265358979...
if we round it to the hundredth we get 3.14
Why do we think 0! = 1?
[tex]4!=4\times3\times2\times1=24\\3!=3\times2\times1=6\\2!=2\times1\\1!=1\\0!=?[/tex]
Notice that when we go from 4! to 3! , we divide by 4.
(Because [tex]4!\div 4 = 4\times3\times2\times1\div4=3\times2\times1=3![/tex] the 4's cancel)
And when we go from 3! to 2! , we divide by 3, and etc.
We can use this pattern to see why 0! = 1.
[tex]4!=4\times3\times2\times1=24\\3! = 4!\div4=24\div4=6\\2!=3!\div3=6\div3=2\\1!=2!\div2=2\div2=1\\0!=1!\div1=1\div1=1[/tex]
And so by following the pattern, we determine that 0! = 1
-------------------------------
Note:
There are no factorials of negative numbers, and we can use the pattern to show why:
[tex]0!=1\\-1!=0!\div0=1\div0=???!!??!?[/tex]
You can't divide a number by 0, therefore -1! doesn't exist, so -2! doesn't exist and so on. So you can't do the factorial of any negative number.
(Or at least there no real solutions to negative factorials)
------------------------
10) Which diagram represents the figure with the greatest volume?
[A]
[C]
4 in
4 in
4 in
4 in
4 in
[B]
[D]
0
4 in
4 in
4 in
Answer:
see below
Step-by-step explanation:
You don't even need to do any math for this one.
All of the other figures will fit inside the first figure with space left over. Obviously, the first figure has the greatest volume.
The Cube is the diagram with the greatest volume which is 64 inch³.
What is the Volume of a solid shape?The volume of a solid body represents the space occupied by the body.
For example:
Volume of Cube = (side)³
Volume of Sphere = 4/3 π (radius)³
Volume of Cylinder = π (radius)² (height)
Volume of Cone = ⅓ pi (radius)² (height)
How to solve the problem?We will just put the value of radius, side, and height in the formula of the Volume of the corresponding diagrams.
Volume of the given Cube = (4)³ = 64 inch³
Volume of the given sphere = 4/3 π (2)³ = 8(4/3)π = 33.51 inch³
as the radius of the sphere is 2 inches, because the diameter of the sphere is 4 inches.
Volume of the given Cylinder = π (2)² (4) =50.26 inch³
as the radius of the Cylinder is 2 inches, because the diameter of the Cylinder is 4 inches.
Volume of the given Cone = ⅓ π (2)² (4) = 16.76 inch³
as the radius of the Cone is 2 inches, because the diameter of the Cone is 4 inches.
Thus, we come to the conclusion that the Cube is the diagram with the greatest volume which is 64 inch³.
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Express 1400 as a product of its prime factors in index form
Answer:
[tex]2^3 X5^2 X7[/tex]
Step-by-step explanation:
Given the number: 1400
A number is said to be prime when it can only be divided by 1 and itself.
We can express 1400 as a product of its prime numbers by gradually decomposing it into smaller units.
[tex]1400=14X100\\14=2X7\\100=10X10=2X5X2X5\\$Therefore:\\1400=2 X 7 X 2 X 5 X 5 X 5\\Reorganising\\1400=2 X 2 X 2 X 5 X 5 X 7\\Therefore, 1400 expressed as a product of its prime factors is:\\1400=2^3 X5^2 X7[/tex]
20% of the people in a community use the emergency room at in one year,find the probability that at most three used the emergency room for a sample of 10 people
Answer:
The probability that at most three used the emergency room for a sample of 10 people is 0.8791.
Step-by-step explanation:
The random variable X can be defined as the number of people in a community using the emergency room.
The probability that a person uses the emergency room is, p = 0.20.
A sample of n = 10 people are selected.
A person using the emergency room is independent of others.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.20.
The probability mass function of X is provided as follows:
[tex]P(X=x)={10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that at most three used the emergency room as follows:
P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
[tex]=\sum\limits^{3}_{x=0}{{10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x}}\\\\=0.10737+0.26844+0.30199+0.20133\\\\=0.87913\\\\\approx 0.8791[/tex]
Thus, the probability that at most three used the emergency room for a sample of 10 people is 0.8791.
What’s the correct answer for this?
Answer:
Arc CR = 90 deg
=> angle CBR = 90 deg
=> angle CBV = 90 deg
=> 3x + 4 = 90
=> 3x = 86
=> x =~28.7 deg
=> Option A is correct
Hope this helps!
:)
Answer:
A: x = 28.7
Step-by-step explanation:
Since VR is the diameter and CB is bisecting it so arcVC= arcCR and
<CBV = <CBR
NOW
3x+4 = 90
3x = 90-4
3x = 86
Dividing both sides by 3
x ≈ 28.7
A method currently used by doctors to screen patients for a certain type of cancer fails to detect cancer in 15% of the patients who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 patients known to this type of cancer is screened using the new method and the method failed to detect the cancer in 8 patients. At the 5% level of significance, can the researchers conclude that the new method is better than the one currently in use? (Can they conclude that the new method fails to detect cancer in less than 15% of the patients who actually have the disease?)
Answer:
A technique presently used through docs to display screen ladies for breast most cancers fails to observe most cancers in 15% of the girls who without a doubt have the disease. A random pattern of eighty girls acknowledged to have breast most cancers are to be screened the use of a new technique that researchers suppose will be capable to realize most cancers greater accurately. At the 0.05 stage of significance, the researchers will be capable to conclude that the new approach is higher than the present day one if the fantastic.
Answer::: greater than 1.645
what is the following quotient? 1/1+sqrt3
Answer:
4 answer
Step-by-step explanation:
The quotient 1 / (1 + √3) is (- 1 +√3) / 2.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 / (1 +√3)
Rationalize the denominator.
1 / (1 +√3) x (1 -√3) / (1 -√3)
{ a² - b² = (a + b) (a - b) ]
(1 -√3) / (1 - 3)
(1 -√3) / -2
-(1 -√3) / 2
(- 1 +√3) / 2
Thus,
The final expression is (- 1 +√3) / 2
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A cylindrical metal pipe has a diameter of 8.4 millimeters
and a height of 10 millimeters. Ahole cut out of the center
has a diameter of 6 millimeters,
What is the volume of metal in the pipe? Use 3.14 for
and round the answer to the nearest tenth of a cubic
millimeter
8.4 mm
© 282.6 mm
271.3 mm
553.9 mm
836.5 mm
thand
Next
Submit
Answer:
C. 271.44 [tex]mm^3[/tex]
Step-by-step explanation:
We need to first find the volume of the pipe, then find the volume of the hole and then subtract the volume of the hole from the volume of the pipe.
The diameter of the pipe is 8.4 mm. This means its radius is:
8.4/2 = 4.2 mm
The height of the pipe is 10 mm
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h - height
Therefore, the volume of the cylinder without the hole is:
[tex]V = \pi * 4.2^2 * 10\\\\V = 554.18 mm^3[/tex]
The diameter of the hole is 6 mm. Its radius is:
6/2 = 3 mm
The volume of the hole is:
[tex]V = \pi * 3^2 * 10\\\\V = 282.74 mm^3[/tex]
The volume is:
554.18 - 282.74 = 271.44 [tex]mm^3[/tex]
Answer:
B. 271.3 [tex]mm^{3}[/tex]
Step-by-step explanation:
Volume of the outer cylinder minus the volume of the inner cylinder returns the volume of the metal outer ring that surrounds the hole.
The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.
The question is incomplete:
The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.
What is the administration fee?
Answer:
$60
Step-by-step explanation:
To calculate the administration fee, first you have to calculate the difference between the two permits and divide that by the month difference that is: 15-12= 3 to know the cost of the monthly fee:
$810-$660= 150
$150/3= $50
Now, you can multiply the monthly fee for 12 to know the total cost of the monthly fee for 12 months and then, subtract this from the cost of a permit purchased for 12 months to find the cost of the one-time administration fee:
$50*12= $600
$660-$600= $60
According to this, the administration fee is $60.
50 POINTS + BRAINLIEST
Use complete sentences to describe the net of a triangular pyramid with an equilateral triangle for a base.
Answer:
The net of a triangular pyramid with an equilateral triangle for the base consists of four triangles, and at least three of them are congruent to each other.
Step-by-step explanation:
Find the Ratio of 250m to 1.5km
Answer:
Step-by-step explanation:
1 km= 1000m
1.5 km = 1 x 1000 + 500
1000 + 500
1500m
1500 m : 250 m
750 m : 125 m
150 m : 25 m
30 m : 5 m
6 m : 1m
0.0
Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as mid-level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.
Construct a 95% confience interval for the percentage of executives that preferred trucks. ( I know for sure that the answer is +or- 6.82%, but I need to know how to get this.)
Answer:
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Step-by-step explanation:
We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.26.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328[/tex]
The 95% confidence interval for the population proportion is (0.192, 0.328).
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Can someone please help me with this question? I really don't get it. Your help would be much appreciated. :) What is the length of CD to the nearest tenth?
Answer:
5.7
Step-by-step explanation:
The altitude of a right triangle divides it into two smaller triangles, all three of which are similar.
ΔABC ~ ΔADB ~ ΔBDC
Writing and solving a proportion:
AD / BD = BD / CD
(x + 3) / 5 = 5 / (2x + 3)
(x + 3) (2x + 3) = 25
2x² + 9x + 9 = 25
2x² + 9x − 16 = 0
x = [ -9 ± √(81 − 4(2)(-16)) ] / 2(2)
x = [ -9 ± √(81 + 128) ] / 4
x = (-9 ± √209) / 4
x = -5.86 or 1.36
Since x can't be -5.86, x = 1.36. So the length of CD is:
CD = 2(1.36) + 3
CD = 5.7
What’s the correct answer for this?
Answer:
the third option
Step-by-step explanation:
the union of two sets of numbers just has to show all the numbers that are in the two sets, meaning if both sets have the same number, it is only shown once in the union
In a sociology course, the professor informed the students of a recent exam ratio of 9:7:2 for As, Bs , and Cs. If 72 students scoring C or better completed the exam l, how many students received Bs?
Answer:
28
Step-by-step explanation:
To solve this, I would first add up the total of the numbers in the ratio.
9 + 7 + 2 = 18
Then, I would divide 72 by that number.
72/18 = 4.
Finally, I would multiply that quotient by 7 because 7 is the number in the ratio for B's.
4 x 7 = 28
Complete the standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Answer:
[tex]\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1[/tex]
Step-by-step explanation:
The equation of the horizontal hyperbola in standard form is:
[tex]\frac{(x-k)^{2}}{a^{2}} - \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
The position of its center is:
[tex]C(x,y) = \left(\frac{-10 + 70}{2}, -15 \right)[/tex]
[tex]C(x, y) = (30,-15)[/tex]
The values for c and a are respectively:
[tex]a = 70 - 30[/tex]
[tex]a = 40[/tex]
[tex]c = 30 - (-11)[/tex]
[tex]c = 41[/tex]
The remaining variable is computed from the following Pythagorean identity:
[tex]c ^{2} = a^{2} + b^{2}[/tex]
[tex]b = \sqrt{c^{2}-a^{2}}[/tex]
[tex]b = \sqrt{41^{2}-40^{2}}[/tex]
[tex]b = 3[/tex]
Now, the equation of the hyperbola is:
[tex]\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1[/tex]
Answer:
The above answer is correct but the 3 should be a 9
Step-by-step explanation:
Plato
Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult. At one of the concerts, each adult brought 444 children with them, and 101010 children attended without an adult. The total ticket sales were \$1{,}730$1,730dollar sign, 1, comma, 730. Which of the following systems of equations can be solved to determine the number of children, ccc, and adults, aaa, who attended the concert?
Answer:
Step-by-step explanation:
Let c represent the number of children that attended the concert.
Let a represent the number of adults that attended the concert.
At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. This means that the number of children that attended is
c = 4a + 10
Tickets for a concert were $5 for each child and $8 for each adult. The total ticket sales were $1730. It means that
5c + 8a = 1730
Therefore, the systems of equations that can be solved to determine the number of children, c, and adults that attended the concert is
c = 4a + 10
5c + 8a = 1730
Answer:
c = 4a + 10
5c + 8a = 1730
Step-by-step explanation:
You took 6 math quizzes. Your scores are: 89, 96, 92, 84, 94, 100. Mrs. Edwards gave you the choice to pick the mean, median, mode or range to be your report card grade. Which one would you pick and why?
Answer:
Median. It has the highest grade.
Step-by-step explanation:
Mean: 92.5
Median: 93
Mode: no mode (all numbers occur only once)
Range: range is 11 (this would be a terrible grade)
Because the median has the highest grade, you would want to pick it.
If you want/ need me to show work or explain just let me know
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What is the value of 6/x+2x,when x=3
Answer:
8
Step-by-step explanation:
6/3 + 2 x 3
6/3 + 6
2 + 6=8
Answer:
[tex]2/3[/tex]
Step-by-step explanation:
[tex]\frac{6}{3x}[/tex]
[tex]\frac{6}{3(3)}[/tex]
[tex]\frac{6}{9} =\frac{2}{3}[/tex]
Kendra found this relationship between the quantities in the table.
1
3
4
2.
150
5
375
y
75
225
300
Multiply x by 7.5 to get y
Which error did Kendra make?
Kendra should have added 75 to the x-values to get the y-values
Kendra should have added 7.5 to the x-values to get the y-values
Kendra should have multiplied the x-values by 75 to get the y-values
Kendra should have multiplied the x-values by 25 to get the y-values
HELP IM TIMED
Answer:
Kendra should have multiplied the x-values by 75 to get the y-values
Step-by-step explanation:
Given
Table
X|| Y
1 || 75
2 || 150
3 || 225
4 || 300
5 || 375
Given that Kendra multiply x by 7.5 to get y
The relationship of x and y can be calculated as thus;
y = rx
Where y and x are the values at the y and x column respectively and r is the constant of proportionality
When y = 75, x = 1.
Plug in these values in the above formula
y = rx becomes
75 = r * 1
75 = r
r = 75
When y = 150, x = 2
150 = r * 2
Multiply both sides by ½
150 * ½ = r * 2 * ½
75 = r
r = 75
When y = 225, x = 3
225 = r * 3
Multiply both sides by ⅓
225 * ⅓ = r * 3 * ⅓
75 = r
r = 75
Notice that r remains 75 and the difference between y values is 75
If you apply these formula on when y = 300 or 375 and when x = 4 or 5, the constant of proportionality will remain The value of 75.
Hence, Kendra mistake is that; Kendra should have multiplied the x-values by 75 to get the y-values
Write a cost function for the cost c to rent a car for d days
Answer:
cost = c*d
Step-by-step explanation:
Unless the cost is calculated by the time (hours) or mileage, we can use the number of days in the calculation.
Everyday is one unit of c, so c times the number of days it is used gives us the cost. Simply multiply the number of days by cost per day to get the total cost.
Write a compound inequality to represent all of the numbers between -4 and 6.
Answer:
-4<X<6
Step-by-step explanation:
Let the number be X
Hence -4<X<6
What is 75/2\3 for my math homework
Step-by-step explanation:
75 ÷ 2/3 = 12.5
This is the correct answer
Answer:
The answer is 225/2 or 112 1/2 or 112.5
Step-by-step explanation:
When a number is divided by a fraction, you have to convert it into multiply by making the fraction upside down :
[tex]75 \div \frac{2}{3} [/tex]
[tex] = 75 \times \frac{3}{2} [/tex]
[tex] = \frac{75 \times 3}{2} [/tex]
[tex] = \frac{225}{2} [/tex]
[tex] = 112 \frac{1}{2} \: or \: 112.5[/tex]
Suppose that the exam scores for students in a large university course are normally distributed with an unknown mean and standard deviation. The scores of 42 randomly sampled students in the course are used to estimate the mean of the population. What t-score should be used to find the 99% confidence interval for the population mean? df...4041424344t0.10…1.3031.3031.3021.3021.301t0.05…1.6841.6831.6821.6811.680t0.025…2.0212.0202.0182.0172.015t0.01…2.4232.4212.4182.4162.414t0.005…2.7042.7012.6982.6952.692 Use the portion of the table above or a calculator. If you use a calculator, round your answer to three decimal places.
Answer:
Critical value t-score=2.701.
Step-by-step explanation:
When we calculate a confidence interval with an unknown population standard deviation, we estimate it from the sample standard deviation and use the t-score instead of the z-score.
The critical value for t depends on the level of confidence and the degrees of freedom.
If the sample size is 42, the degrees of freedom are:
[tex]df=n-1=42-1=41[/tex]
For a confidence level of 99% and 41 degrees of freedom, the critical value of t is t=2.701.
Rebecca made an equation that models the height of a tree since she moved in. The height of the tree, h=3t+40 where H=height (in feet) and t=years. How big was the height of the tree when she moved in?
Answer:
40 feet
Step-by-step explanation:
The number of years since she moved in when she just moved in is 0,
thus, t=0
So,
H=3*0+40
H=40 feet
The height of the tree when Rebecca just moved in was 40 feet
Gabrielle draws an angle that measures 134º.
She then draws a ray that divides the angle into two non-overlapping angles,
The measure of one angle is 85°,
Part A
Which equation can Gabrielle use to find the measure of the other angle?
A. 134° +85° = a
B 1340 + 2 = a
C. 134° -85° = a
D. 134 +90° = a
00:00
Part B
What is the measure of the other angle? Enter your answer in the box.
Answer:
134 - 85 = a
a = 49
Step-by-step explanation:
The sum of the two angles is 134
a+ 85 = 134
134 - 85 = a
49 =a
Does anyone know the answer?
Answer:
AB = 4.41
Step-by-step explanation:
→You are given the adjacent side and need to find the hypotenuse. For this, we use cos.
→Set it up, like so:
[tex]cos25=\frac{4}{x}[/tex]
→To get rid of the x in the denominator, multiply everything by x:
[tex]x(cos25=\frac{4}{x})[/tex]
[tex]xcos25 = 4[/tex]
→Divide both sides by cos25:
x = 4.413
→Round to nearest hundredth:
x = 4.41
