Answer:
The original number was 36.7.
Step-by-step explanation:
Multipliers:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
In this question:
The original value is x.
Increased by 28%, so we have that 1 + (28/100) = 1.28x. Equals 47. We have to find x.
1.28x = 47
x = 47/1.28
x = 36.7
The original number was 36.7.
An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.
The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2
h and k are the center point and r is the radius.
In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.
Center (-6,7)
Radius = 9
The required center is [tex](-6,7)[/tex] and the radius is 9 units.
Given equation is,
[tex](x + 6)^2 + (y-7)^2 = 81[/tex]....(1)
Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,
[tex](x-a)^2+(y-b)^2=r^2[/tex]...(2)
We can write the given equation as,
[tex](x + 6)^2 + (y-7)^2 = (9)^2[/tex]
Comparing equations (1) and (2) we get,
The Centre of the given circle is [tex](-6,7)[/tex]
The radius of the given circle is 9 units.
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a bag of sweets contains only two different flavours strawberry and orange. the probability that a sweet is strawberry is 0.8 what is the probability that a sweet is orange falvour
Answer:
0.2
Step-by-step explanation:
total = 1.0
strawberry = 0.8
1-0.8 =0.2
Answer:
0.2 is the probability of orange sweet.
Mason is weighing his dog on a scale that has increments of 0.1 kilograms (kg). He measures his dog's weight as 35.7 kg. How should Mason express his dog's weight, including the uncertainty?
a. 35.7+0.1 kg
b. 35.7−0.1 kg
c. 35.7±0.05 kg
d. 35.7±0.5 kg
Answer:
35.7±0.05 kg
Step-by-step explanation:
Including the uncertainty, the mass of dog is -
35.7 + 0.1 kg.
We have Mason's Dog.
We have to determine how should Mason express his dog's weight, including the uncertainty.
What is Uncertainty in Physics?The uncertainty is the experimenter's best estimate of how far an experimental quantity might be from the true value.
According to the question -
The scale has increments of 0.1 kilograms (kg).
Mason's actual weight - 35.7 kg
Therefore, including the uncertainty, the mass of dog is -
35.7 + 0.1 kg
Hence, including the uncertainty, the mass of dog is -
35.7 + 0.1 kg
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What is the value of x in the equation
Answer:
It is b.
Step-by-step explanation:
0.7 x -3 = -2.1 and -2.1 - 1.4= -3.5
please branliest!!!!
Need answer ASAP please!! Will give brainliest!
Solve each equation by taking square roots.
1. 6r^2=-108
2. 9p^2-8=-58
Answer:
15) A) {3i√2, -3i√2}
16) C) {5i√2/3, -5i√2/3}
Step-by-step explanation:
15)
[tex]6r^2=-108\\\\r^2=\dfrac{-108}{6}=-18\\\\r=\pm\sqrt{-18}\\\\\boxed{r=\pm3i\sqrt{2}}[/tex]
__
16)
[tex]9p^2-8=-58\\\\9p^2=-50\qquad\text{add 8}\\\\p^2=-\dfrac{50}{9}\qquad\text{divide by 9}\\\\p=\pm\sqrt{-\dfrac{50}{9}}\qquad\text{take the square root}\\\\\boxed{p=\pm\dfrac{5\sqrt{2}}{3}}[/tex]
A cylinder has a base diameter of 14m and a height of 15m. What is its volume in
cubic m, to the nearest tenths place?
Answer:
2310m^3
Step-by-step explanation:
base area which is the circle = πr^2
But diameter, d = 14, r = 14/2 = 7
area = π × (7)^2 = 22/7 × 49 = 22 × 7 = 154
Volume = base area × height
= 154 × 15 = 2310
Answer:
2309.1
Step-by-step explanation:
Deltamath
How do you find the domain of functions, I’d just like someone to explain it, that’s where I get lost, 30 points btw
Explanation:
The domain is the horizontal extent of the graph of the function. It is the set of all values of the independent variable for which the function is defined.
In a table or list of (x, y) or (x, f(x)) values the domain is the list of x-values.
On a graph, the domain is the horizontal extent of the graph, excluding any "holes" or vertical asymptotes. (The function is "undefined" at those places.)
__
For a polynomial, the domain is generally "all real numbers."
For rational functions, the domain always excludes any x-values that make any denominator be zero.
For functions such as logarithms or roots, the domain is the set of values for which the function is defined. Even roots (square root, 4th root, ...) are only defined for non-negative numbers. Logarithms are only defined for positive numbers.
__
In some problems, a model is often used that is defined for all values of the independent variable. For example, a height function may be modeled using a quadratic: h(t) = -4.9t^2 +30t +6. This is defined for all values of t, but the "practical domain" is the set of values of t ≥ 0 and before h(t) = 0. That is, we don't care about negative time or negative height.
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
No because the product of their slopes is not -1
In the attached file
Which is the value of this expression when a = 5 and k = negative 2?
(StartFraction 3 squared a Superscript negative 2 Baseline Over 3 a Superscript negative 1 Baseline EndFraction) Superscript k
From what I see in the problem, the expression is
[tex](\frac{3^a^2}{3a^-1} )^k[/tex]
To solve, plug in a and k.
[tex](\frac{3^(5)^2}{3*5^-1} )^-2[/tex]
3*5^2=75
(3*5)^-1 = 1/15
[tex]75 / \frac{1}{15} = 5[/tex]
5^-2 = 1/25
What numbers are missing from this pattern 36,2,13,21,?,?,?,?,36,2,13,21
Answer:
36,2,13,21
Step-by-step explanation:
At its simplest, it is a repeating sequence of 4 numbers:
36,2,13,21
So, those are the four missing numbers.
Find the volume of the pentagonal prism below. B = 52 m²
7.5 m
B = 52 m2
195 m
59.5 m
130 m
23
B90 m
Answer:
390 m^2
Step-by-step explanation:
52(7.5)=390
Select the correct answer.
Identify the axis of symmetry of the function graphed below.
Answer:
D. x = -1.
Step-by-step explanation:
I have attached an explanation to your problem. Please see the attachment below.
Answer:
x= -1
Step-by-step explanation:
it is always the x value of where the vertex is!
I want brainliest plz
Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.06. If 280 are sampled, what is the probability that the sample proportion will be less than 0.09? Round your answer to four decimal places.
Answer:
[tex]\mu_{\hat p}= 0.06[/tex]
[tex] \sigma_{\hat p}= \sqrt{\frac{0.06*(1-0.06)}{280}}= 0.0142[/tex]
And we want to find this probability:
[tex] p(\hat p <0.09)[/tex]
[tex] z = \frac{p \mu_{\hat p}}{\sigma_{\hat p}}[/tex]
[tex] z = \frac{0.09-0.06}{0.0142}= 2.114[/tex]
And we can find this probability:
[tex] P(z<2.114)[/tex]
And using the normal table or excel we got:
[tex] P(z<2.114)= 0.9827[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 280[/tex] represent the sample size
[tex] p =0.06[/tex] represent the true proportion
The sample proportion can be approximated with this distribution:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}})[/tex]
The mean is given by:
[tex]\mu_{\hat p}= 0.06[/tex]
And the deviation is given by:
[tex] \sigma_{\hat p}= \sqrt{\frac{0.06*(1-0.06)}{280}}= 0.0142[/tex]
And we want to find this probability:
[tex] p(\hat p <0.09)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{p \mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z = \frac{0.09-0.06}{0.0142}= 2.114[/tex]
And we can find this probability:
[tex] P(z<2.114)[/tex]
And using the normal table or excel we got:
[tex] P(z<2.114)= 0.9827[/tex]
The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negative x squared Baseline comma where x represents time in years. The total profit in year 2 that the invention is in operation is $ 25 comma 000. Find the total profit function Upper P (x ). Round to the nearest thousandth if necessary.
Answer:
The function is [tex]P(x) = \frac{1}{2} e^{-x^2} +0.016[/tex]
Step-by-step explanation:
From the question we are told that
The rate of growth is [tex]P'(x) = xe^{x} - x^2[/tex]
The total profit is [tex]P(2) =[/tex]$25,000
The time taken to make the profit is [tex]x = 2 \ years[/tex]
From the question
[tex]P'(x) = xe^{-x^2}[/tex] is the rate of growth
Now here x represent the time taken
Now the total profit is mathematically represented as
[tex]P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,[/tex]
So using substitution method
We have that
[tex]u = - x^2[/tex]
[tex]du = 2xdx[/tex]
So
[tex]p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du[/tex]
[tex]p(x) = {\frac{1}{2} [ e^{-u}} +c ][/tex]
[tex]p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c[/tex] recall [tex]u = - x^2[/tex] and let [tex]\frac{1}{2} c = Z[/tex]
At x = 2 years
[tex]P(x) =[/tex]$25,000
So
Since the profit rate is in million
[tex]P(x) =[/tex]$25,000 = [tex]\frac{25000}{1000000} =[/tex]$0.025 millon dollars
So
[tex]0.025 = {\frac{1}{2} e^{-2^2}} + Z[/tex]
=> [tex]Z = 0.025 - {\frac{1}{2} e^{-2^2}}[/tex]
[tex]Z = 0.016[/tex]
So the profit function becomes
[tex]P(x) = \frac{1}{2} e^{-x^2} +0.016[/tex]
Alonzo and Mitra wanted to share a pizza. Mitra ate of the pizza, and Alonzo ate of the pizza.
How much more pizza did Alonzo eat than Mitra?
Answer:
Alonzo ate 1/2 more than Mitra.
Step-by-step explanation:
In this question, you are supposed to find how much more Alonzo ate. We solve that like this:
Steps:
- Set up the Equation:
- 1/4 + ? = 3/4
- The question mark represents the answer.
- Inverse Operations:
- Change 1/4 + ? = 3/4 to 3/4 - 1/4 = ?
- Since Subtraction is the opposite of Addition, we flip the equation.
- Solve:
- [tex]\frac{3}4} -\frac{1}{4} =\frac{2}{4}[/tex]
- Then Simplify:
- [tex]\frac{2}{4} =\frac{1}{2}[/tex]
So, Alonzo ate 1/2 more than Mitra, or C.
Hope this helps! Good luck!
A rectangular prism has a length of 17cm, a height of 20cm, and a width of 18cm.
What is its volume, in cubic cm?
Answer:
6120 cm³
Step-by-step explanation:
You want the volume of a rectangular prism 17 cm by 20 cm by 18 cm.
VolumeThe volume of a rectangular prism is given by the formula ...
V = LWH
Using the given values for length, width, and height, we find the volume to be ...
V = (17 cm)(18 cm)(20 cm) = 6120 cm³
The volume of the prism is 6120 cubic centimeters.
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When solving a quadratic, how can x equal 2 different things? What is x?
Answer:
X = unknown
The highest degree of x is 2 .
Step-by-step explanation:
First of all x is the unknown variable to be determined by solving quadratically
Quadratic equation was chooses because of the degree of x.
The highest degree of x is 2 .
That's the the reason why the value of x will always be double.
If solving linear equation that has degree one, the value of x is one
If solving polynomial, the value of x will be 3 above.
please help the Marshmello
So the value of X is 2.
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
[tex]x = 2[/tex]
First answer is correct
Step-by-step explanation:
[tex]9 = 1 + 8x - 8 \\ 9 - 1 + 8 = 8x \\ 16 = 8x \\ \frac{16}{8} = \frac{8x}{8} \\ x = 2[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A student researcher measured the cadmium (Cd2+) content in a standard reference material (SRM) using graphite furnace atomic absorption spectrometry (GFAAS). With 7 replicate measurements, the researcher determined a mean Cd2 concentration of 2.899 ppb with a standard deviation of 0.001 ppb. Calculate the 99% confidence interval for this sample. Enter your answer with three significant figures.
Answer:
The 99% confidence interval for this sample mean is between 2.895 ppb and 2.903 ppb.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.7074
The margin of error is:
M = T*s = 3.7074*0.001 = 0.004
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.899 - 0.004 = 2.895 ppb.
The upper end of the interval is the sample mean added to M. So it is 2.899 + 0.004 = 2.903 ppb.
The 99% confidence interval for this sample mean is between 2.895 ppb and 2.903 ppb.
How would I graph y=9x+4
Find the surface area of the rectangular prism.
6 yd
3 yd
1 yd
Answer:
54 yd²
Step-by-step explanation:
The surface area of the prism is the sum of the areas of its faces. Opposite faces have the same area, so we can write the formula as ...
SA = 2(LW +WH +LH) = 2(LW +H(L +W))
Filling in the numbers, we have ...
SA = 2(6·3 +1(6 +3)) = 2(18 +9) = 54 . . . . square yards
The area is 54 square yards.
Whats the point slope equation
Answer:
y-4 = 8/7(x-4)
Step-by-step explanation:
formula is y-y=m(x-x) just substitute the numbers in
c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. Choose the correct answer below. A. The analyst did not make an error. The actual value was 55.3 points, which is close to 52.5. B. The analyst made a Type I error. The actual value was 55.3 points, which is greater than 52.5. C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5. D. The analyst made a Type II error. The actual value was 55.3 points, which is close to 52.5. E. The analyst made a Type I error. The actual value was 55.3 points, which is close to 52.5.
Answer:
Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
Step-by-step explanation:
Answer:
Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
Step-by-step explanation:
The null hypothesis was the applicants last year score, on average was 52.5 points.
Conclusion: She fails to reject the null hypothesis that the mean is 52.5 points.
At the end of the year, they find that the candidates this year had a mean of 55.3 points.
A type II error occurs when the researcher fails to reject the null hypothesis when it is false. Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
the radius of a mini basketball is 4 inches. what is the volume rounded to the nearest tenth?
Answer:
268.08 inches3
Step-by-step explanation:
the volume rounded to the nearest tenth is 268.08 in³.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
given the radius of a basketball is 4 inches.
Since basketball has the shape of a sphere,
thus from the general formula of the volume of the Sphere:
Volume = 4/3 πr³
Where r is the radius
in our case
r = 4
Thus volume = 4/3 π 4³
The volume of basketball = 268.08 in³
therefore, the volume of the given basketball is 268.08 in³.
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Help please. Will put brainliest
Answer:
17,7501737Step-by-step explanation:
A suitable table or calculator is needed.
One standard deviation from the mean includes 68.27% of the total, so the number of bottles in the range 20 ± 0.16 ounces will be ...
0.6827·26,000 = 17,750 . . . . . within 20 ± 0.16
__
The number below 1.5 standard deviations below the mean is about 6.68%, so for the given sample size is expected to be ...
0.66799·26,000 = 1737 . . . . . below 19.76
_____
Comment on the first number
The "empirical rule" tells you that 68% of the population is within 1 standard deviation (0.16 ounces) of the mean. When the number involved is expected to be expressed to 5 significant digits, your probability value needs better accuracy than that. To 6 digits, the value is 0.682689, which gives the same "rounded to the nearest integer" value as the one shown above.
1. Nicole purchased new lawn furniture for $279.90. She used a coupon to
get a 15% discount. What was the final purchase price, excluding sales tax
of the lawn furniture?
Answer:
$237.92
Step-by-step explanation:
0.85 x 279.90 = 237.915 = ~237.92
Write the largest one digit,two digit,three digitnumbers and compare them with both signs< >
Answer:
[tex]9<99<999[/tex]
[tex]999>99>9[/tex]
Step-by-step explanation:
The largest one digit number=9The largest two digit number=99The largest three digit number=999We have that:
9<9999<999If a<b and b<c, then a<b<c.
Combining the two inequalities, we obtain: [tex]9<99<999[/tex]
In reverse, we can also write this as:
[tex]999>99>9[/tex]
The mean age of 5 people in a room is 32 years.
A person enters the room.
The mean age is now 36.
What is the age of the person who entered the room?
Answer:
56
Step-by-step explanation:
If you could give me a thanks, that would be much appreciated.
Solve the inequality (13+2x) -4>39 Express the solution in set notation
Answer:
x > 15
Step-by-step explanation:
simplify both sides of the inequality
2x + 9 > 39
subtract 9 from both sides
2x + 9 - 9 > 39 -9
2x > 30
divide both sides by 2
2x/2 > 30/2
x > 15
1. A crash repair bill comes to $1380.00. How much is 10% of
the bill? What is the final bill once 10% is taken off?
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Answer:
1. 10% of the bill is $138. The final bill once 10% is taken off is $1242.
2. 20% of the total is $34.10. The final total once the 20% is taken off is $136.4
Step-by-step explanation:
1. A crash repair bill comes to $1380.00. How much is 10% of the bill? What is the final bill once 10% is taken off?
To find how much is 10% of the bill, we multiply the bill by 0.1
0.1*1380 = 138
10% of the bill is $138.
To find the final bill, we subtract the initial bill by 10%.
1380 - 138 = 1242
The final bill once 10% is taken off is $1242.
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Same logic as above.
0.2*170.50 = 34.1
20% of the total is $34.10.
170.50 - 34.1 = 136.4
The final total once the 20% is taken off is $136.4