Step-by-step explanation:
Let $p be the original price.
[tex](1 - 25\%)p = 30 \\ \frac{75}{100}p = 30 \\ p = 40[/tex]
∴ The original price is $40.
Which angle is an acute angle?
A. An angle measuring 325°
B. An angle measuring 265°
C. An angle measuring 125°
D. An angle measuring 85°
Answer:
The answer is Option D
Step-by-step explanation:
Option D is the right answer since 85° is a acute angle. Acute angles are angles below 90°
Hope this helps!
Have a good day
If two figures that are similar have a factor of 1.2, the second figure is:
A quick answer and no link please!
Answer:
enlarged
Step-by-step explanation:
imagine there are two figures, figure A and B. figure A has a length of 10cm and the scale factor is 1.2
the length of figure B = 10 X 1.2 = 12
Figure B has a longer length than figure A. thus figure B is an enlarged version of figure A.
Conversely, if the factor is 0.2
the length of figure B = 10 X 0.2 = 2cm
the length of figure B is less than that of figure A. Thus, figure B is a scaled image of A
A polling company conducted a survey asking 40 fourth year students from Ohio and 33 fourth-year students from Pennsylvania about on average, how many hours they spend on the computer per week. Ohio had an average of 52, while Pennsylvania had an average of 33. Ohio and Pennsylvania have standard deviations of 7.22 and 10.11 respectively. Construct a 99.9% confidence interval for the difference between these results.
Answer:
The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of variances.
Ohio had an average of 52, standard deviation of 7.22, sample of 40.
This means that [tex]\mu_O = 52, s_O = \frac{7.22}{\sqrt{40}} = 1.1416[/tex]
Pennsylvania had an average of 33, standard deviation of 10.11, sample of 33.
This means that [tex]\mu_P = 33, s_P = \frac{10.11}{\sqrt{33}} = 1.76[/tex]
Distribution of the difference:
[tex]\mu = \mu_O - \mu_P = 52 - 33 = 19[/tex]
[tex]s = \sqrt{s_O^2 + s_P^2} = \sqrt{1.1416^2 + 1.76^2} = 2.1[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.999}{2} = 0.0005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.0005 = 0.9995[/tex], so Z = 3.29.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 3.29*2.1 = 6.91[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 19 - 6.91 = 12.09 hours per week
The upper end of the interval is the sample mean added to M. So it is 19 + 6.91 = 25.91 hours per week.
The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.
Find the area of the figure
Answer:
288.62
Step-by-step explanation:
Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch. She slipped and spilled 1/4 of the lemonade in the pitcher. What fraction of a gallon of lemonade did she spill?
Answer:
Susan spilled 1/6 of a gallon of lemonade.
Step-by-step explanation:
Since Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch, and she slipped and spilled 1/4 of the lemonade in the pitcher, to determine what fraction of a gallon of lemonade did she spill the following calculation must be performed:
2/3 = 0.6666
0.666666 x 1/4 = X
0.166666 = X
0.166666 = 1/6
Therefore, Susan spilled 1/6 of a gallon of lemonade.
Simplify the polynomial, then evaluate for x = 2 . x + 3x ^ 2 + 2x - 3 - 4x ^ 2 + 6
Answer:
-x^2+3x+3
Step-by-step explanation:
if the evaluated answer is correct (but my answer above is correct) it would be -4+6+3 then the answer would be 5 but I am not sure
56 times a number minus 13 is equal to 6 less than the number.
Step 2 of 2: Solve the equation for z. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two places.
Answer:
Z = 19/56OR Z = 0.34Step-by-step explanation:
The steps in the photo above
I hope that is useful for you :)
Find the coefficient of x^2 in the expansion of (2x - 1)^5.
Answer:
So, the coefficient of the x^2 -term is 80
Step-by-step explanation:
so we need to simplify it:
#10(x^2)(2^3) = 10(x^2)(8) = 80x^2
A cube has an A on 3 sides and a B on 3 sides. Rolling it 50 times results in 17 A's and 33 B's.
Using this observed probability, how many A's would be rolled in 750 tries?
when did the alec meet the stallion ?
Answer:
The Black Stallion, known as the Black or Shêtân, is the title character from author Walter Farley's bestselling series about the Arab stallion and his young owner, Alec Ramsay. The series chronicles the story of a sheikh's prized stallion after he comes into Alec's possession, although later books furnish the Black's backstory. Shaytan (under various transliterations) is the Arabic word for "devil".
help please!!!!!!!!!!!!!!!!!!! very important
Answer:
i got B for my answer
Consider a situation in which P(A), = 1/8, P(C) = 1/4, and P(A and B) = 1/12. what is P(V and C)
Answer:
1/6
Step-by-step explanation:
just did on edg
Which table of values represents a linear function?
A,B,C,D
Answer:
c as they give the line of the graph
What is the graph of the following parametric equation? x = sqrt(t) and y = 2t - 3
(pls include a graph answer!)
Answer:
Th final equation is [tex]Y = 2X^2 -3[/tex]
The graph is attached
Step-by-step explanation:
Given
[tex]X = \sqrt{t} \\t = X^2[/tex] --- Eq (1)
and [tex]Y = 2t -3[/tex] --- Eq (2)
Substituting the value of "t" from Eq (1) into Eq (2), we get -
[tex]Y = 2X^2 -3[/tex]
The graph for the equation is attached here with
The Cartesian form of the parametric equation is y = 2x² – 3 and the graph will be a parabola.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have parametric functions:
x = √t ⇒ x² = t
y = 2t—3
Plug t = x² in the other equation, we get:
y = 2x² - 3
The graph will be a parabola.
Thus, the Cartesian form of the parametric equation is y = 2x² – 3 and the graph will be a parabola.
Learn more about the parametric function here:
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A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s=−16t2+192t. After how many seconds will the ball be 560 feet from the ground?
Answer:
t=7seconds or 5seconds
Step-by-step explanation:
s=-16t^2 +192t
let s=560ft
560=-16t^2 +192t
16t^2 -192t+560=0
16(t^2-12t+35)=0
(t^2 -12t +35)=0
factoring it ,it will give
(t-7)(t-5)=0
solving for t
t-7=0 or t-5=0
t=7s or t=5s
Translate the expressions with rational exponents into radical expressions, then simplify.
Please show step by step so I can understand
Find the 9th term of the geometric sequence show below
Answer:
40x^20
Step-by-step explanation:
Each sequence the x value doubles.
Each sequence the x exponent goes up by 5
what is the mean median mode and range of 98,89,76,93,89?
Answer:
Mean: 89
Median: 89
Mode: 89
Range: 22
Step-by-step explanation:
Answer:
89
Step-by-step explanation:
Mean-89
Median-89
Mode-89
2(v + 1). Simplify the expression
Answer:
2v+2
Step-by-step explanation:
Two workers can finish building a play set in 18 hours. How long will it take 4 workers to build 3 play sets
Answer:
it will take 4 workers 27 hours to build 3 playsets.
Step-by-step explanation:
Given;
two works to build 1 play set in 18 hours
If a worker works at the same rate, he will finish a playset as follows;
2 worker ---------> 18 hours
1 worker -----------> ?
1 worker = 2 x 18 hours = 36 hours for 1 playset
4 workers will take ³⁶/₄ hours for 1 playset
4 workers --------------> 9 hours for 1 playset
For 3 playsets, 4 workers will take 3 x 9 hours = 27 hours.
Therefore, it will take 4 workers 27 hours to build 3 playsets.
If 19.3% of children and adolescents are obese (14.4M), what is the total number of children and adolescents overall? Please i need help
Answer:
74,611,399
Step-by-step explanation:
Percentage of obese children and adolescent = 19.3%
19.3% = 14.4 million
The overall number of children and adolescent equals a total percentage of 100%
Hence,
If 19.3 % = 14.4 million
100% = x
Cross multiply :
19.3% x = 100% * 14.4 million
0.193x = 14400000
x = 14400000 / 0.193
x = 74611398.964
Total number of children and adolescent = 74,611,399
How much money will there be in an account at the end of 8 years if $9,000 is deposited at 3% interest compounded semi-annually? (Assume no withdrawals are made.)
Answer:
8730
Step-by-step explanation:
What is 108 divided by 8
Answer:
13.5
Step-by-step explanation:
Mark me brainliest!
Or 13 with a remainder of 5
13R5
or
13 5/8
The quotient is 13 and the remainder is 4 for the given statement.
When we divide 108 by 8, we find:
108 ÷ 8 = 13 remainder 4
The quotient is 13 and the remainder is 4.
Therefore, 108 divided by 8 is equal to 13 with a remainder of 4.
Learn more about Mathematical operations here:
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Simplify 79.5-2.58 x (3.63-1.63) to the third power
Answer:
a
Step-by-satep explanation:
Change to slope-intercept form. Then find the y-intercept, first point, and second point.
x + 3y > 9
slope intercept form
y -Intercept
first point (let x=0)
second point
Answer:
[tex]x + 3y > 9 \\ 3y > - x + 9 \\ y > - \frac{1}{3} x + 3 \\ y - intercept \: is \: 3 \\ first \: point = 3 \\ second \: point \: = 9[/tex]
Please help with these questions
Answer:
...... ....... ........
Multiply 4x (x - 3)
I need help badly please
Answer:
[tex] {4x}^{2} - 12x[/tex]
Answer:
4x² - 12x
Step-by-step explanation:
Multiply 4x by each term inside the parentheses
4x(x) = 4x²
4x(-3) = -12x
Put the terms back into order
4x² - 12x
Solve the inequality. -4x < 24
Answer:
x > -6
Step-by-step explanation:
1) Divide both sides by -4
x > - [tex]\frac{24}{4}[/tex]
2) Simplify and solve to get answer.
x > -6.
Helppppp pleSeeeeeeeee
Answer: C
Step-by-step explanation: Hope this help :D
i need help please it's due today
Step-by-step explanation:
work is on the paper for you, somthing that might help you with your future with math is PEMDAS always do exponents first when it's an equation like your first, second, and third question. I hope this helped.