Answer:
Step-by-step explanation:
The number of times that each song is played is reducing in arithmetic progression. We would determine the total number of time for plating all the songs in a week by applying the formula for determining the sum of the n terms in an arithmetic sequence. It is expressed as
Sn = n/2(2a + (n - 1)d
Where
d represents the common difference
n represents the number of terms
a represents the first term of the sequence
Sn represents the sum of n terms if the sequence.
From the information given,
a = 60
n = 60
d = - 1
Sn = 60/2(2 × 60 + (60 - 1)-1)
Sn = 30(120 - 59)
Sn = 1830 times
The 60 songs are played for 1830 times in a week. If each song takes 3 minutes to play, then the total time taken to play the songs for 1830 times in a week is
3 × 1830 = 5490 minutes
7 days = 1 week
24 hours = 1 day
60 minutes = 1 hour
The number of minutes in a week is
7 × 24 × 60 = 10080 minutes
The station also has 24 ten-minute news breaks each day. The number of minutes of break for each day is
24 × 10 = 240 minutes
The amount of break time in a week is
240 × 7 = 1680 minutes
If the remaining minutes is meant for advertising, then the number if minutes available for advertising is
10080 - (5490 + 1680) = 2910 minutes
1 minute = 60 seconds
2910 minutes = 2910 × 60 = 174600 seconds
If the station charges $100 for every 30 seconds of advertising, then the amount that they take in each week(for 174600 seconds) is
(174600 × 100)/30 = $5820000
(50 POINTS) Complete the square to find the center and radius of each circle.
Answer:
Rewrite in standard form to find the center (h,k) and radius r.
Center: (−1,−2)
Radius: √6
Rewrite in standard form to find the center (h,k) and radius r.
Center: (3/2,6)
Radius: 11/2
Rewrite in standard form to find the center (h,k) and radius r.
Center: (3,−7)
Radius: 8
Rewrite in standard form to find the center (h,k) and radius r.
Center: (0,10)
Radius: 9
Rewrite in standard form to find the center (h,k) and radius r.
Center: (−4,−4)
Radius: 4√2
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. if you select a sample of 100 light bulbs and find mean bulb life is 490 hours. Perform the hypothesis test at the significance level of 0.01. Referring to Scenario 9-10, what is the test statistic
Answer:
We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.
Step-by-step explanation:
We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.
You select a sample of 100 light bulbs and find mean bulb life is 490 hours.
Let [tex]\mu[/tex] = population mean light bulb life.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 500 hours {means that the population mean light bulb life is at least 500 hours}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 500 hours {means that the population mean light bulb life is below 500 hours}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean bulb life = 490 hours
σ = population standard deviation = 50 hours
n = sample of light bulbs = 100
So, the test statistics = [tex]\frac{490-500}{\frac{50}{\sqrt{100} } }[/tex]
= -2
The value of z test statistics is -2.
Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.
Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the population mean light bulb life is at least 500 hours.
Show your work and explain in full sentence how 4 2/6 is equivalent to 3 8/6.
Answer:
Step-by-step explanation:
The given fractions that we are comparing are expressed as mixed numbers. It means that each is made up of whole numbers and fractions. We would convert each mixed number to improper fraction. By converting to improper fraction, we would multiply the whole number by the denominator and add the product to the numerator. The fraction would be the ratio of the result to the denominator.
Considering 4 2/6, it becomes
(4 × 6) + 2) = 26/6
Considering 3 8/6, it becomes
(3 × 6) + 8)/6 = 26/6
Therefore, they are equivalent
An international company has 15,900 employees in 1 country if this represent 22.3% of the company's employees how many employees does it have entitled
Answer:
33.6% of X = 26800
X = 26800 / 33.6%
= 26800 / 0.336
= 79762
Note the answer is rounded
Step-by-step explanation:
If Mario puts $12,000 in a bank account that pays 4% interest quarterly, how much will he have after 3 years?
Answer:
[tex] P=12000, r= 0.04, t=3[/tex]
And n=4 since the rate is compounded quarterly, so then replacing this info we got:
[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]
So then Mario will have about $13521.9 after the 3 years with the rate of interest used.
Step-by-step explanation:
For this case we can use the formula for future value based on a compound interest given by:
[tex] A= P (1+ \frac{r}{n})^{nt}[/tex]
Where A represent the future value, P the present value or the inversion r is the rate of interest on fraction, n the number of times that the rate of interest is compounded in a year and t the number of years.
For this case we know this:
[tex] P=12000, r= 0.04, t=3[/tex]
And n=4 since the rate is compounded quarterly, so then replacing this info we got:
[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]
So then Mario will have about $13521.9 after the 3 years with the rate of interest used.
42% of jacksons halloween candy from last year was chocolate. what fraction of his candy's chocolate
Answer:
21/50
Step-by-step explanation:
Given that Jackson's sweets from last Halloween from last year was 42% chocolate, we can assume he had a total of 100 sweets.
Out of 100 sweets, 42 pieces are chocolate, so:
42/100
When simplifying this fraction into its simplest form, the most you can do is divide the numerator(top) and denominator(bottom) by 2.
Your result would be 21/50
Hope this helps!
An art collector paid $7,000 for two paintings, a portrait and a landscape, at the same auction. Each painting cost $3,500.
The collector predicts that the value of the landscape painting will increase by 15% per year. If she is correct, what will its value
be one year after the date of purchase?
Answer:
4025
Step-by-step explanation:
3500×0.15=525
3500+525= 4025
Answer:
4025
Step-by-step explanation:
Hope this helps
Which ratio is less than StartFraction 15 Over 24 EndFraction?
One-half
StartFraction 7 Over 8 EndFraction
StartFraction 19 Over 24 EndFraction
StartFraction 6 Over 8 EndFraction
Answer:
[tex]\frac{1}{2}[/tex] (one-half)
Step-by-step explanation:
Given: Fraction is [tex]\frac{15}{24}[/tex]
To find: the correct option
Solution:
A fraction represents part of a whole.
An improper fraction is a fraction in which numerator is greater than the denominator and a proper fraction is a fraction in which numerator is less than the denominator.
[tex]\frac{1}{2}=\frac{1\times 12}{2\times 12}=\frac{12}{24}< \frac{15}{24}\\\frac{7}{8}=\frac{7\times 3}{8\times 3}=\frac{21}{24}> \frac{15}{24}\\\frac{19}{24}> \frac{15}{24}\\\frac{6}{8}=\frac{6\times 3}{8\times 3}=\frac{18}{24}> \frac{15}{24}[/tex]
So, ratio [tex]\frac{1}{2}[/tex] is less than the given fraction [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
Find the equation of a circle with the Endpoints of a diameter: (11, −5), (3, 15)
Answer:
(x - 7)² + (y - 5)² = 116
Step-by-step explanation:
equation of a circle:
(x - h)² + (y - k)² = r²
where (h,k) is the centre and r is the radius
centre is the midpoint of the diameter:
(h,k) = (11+3)/2 , (-5+15)/2
(h,k) = (7,5)
diameter = sqrt[(15--5)² + (3-11)²]
diameter = sqrt(464) = 4sqrt(29)
radius = ½ diameter
radius = 2sqrt(29)
r² = 116
equation:
(x - 7)² + (y - 5)² = 116
Answer:
[x-7]^2 + [y-5]^2= 116
Step-by-step explanation:
General equation of a circle is
[x2 - xo]^2 + [y2- yo]^2 = r^2
Where xo and yo are coordinates of the circle at the origin.
But xo = [x2 + x1]/2
= 11 + 3 / 2 = 7
yo = [y2 + y1] / 2 = [-5 + 15] /2 = 5
x2= 11, x2= 3; y1= -5, y2= 15
[11-7]^2 + [15-5]^2 =
16+ 100=116 = r^2
From the expression below;
[x2-xo]^2 + [y2-yo] ^2 = r^2
[x1-xo]^2 + [y1-yo] ^2 = r^2
[x-7]^2 + [y-5]^2= 116
heccin hurry
The model below represents 4 x + (negative 4) = negative 2 x + 8. 4 long green tiles and 4 square red tiles = 2 long red tiles and 8 square green tiles. What is the value of x when solving the equation 4 x + (negative 4) = negative 2 x + 8 using the algebra tiles? x = negative 4 x = negative 2 x = 2 x = 4
Answer:
x = 2Step-by-step explanation:
Given the equation model 4x+(-4) = -2x+8
To find the value of x, the following steps must be followed
[tex]4x+(-4) = -2x+8\\4x-4 = -2x+8\\subtracting\ 8\ from\ both\ sides\\4x-4-8=-2x+8-8\\4x-12=-2x\\4x+2x=12\\6x=12\\x=\frac{12}{6}\\ x = 2[/tex]
The value of x is 2
Question:
The model below represents 4x + (-4) = -2x + 8.
4 long green tiles and 4 square red tiles = 2 long red tiles and 8 square green tiles.
What is the value of x when solving the equation 4x + (-4) = -2x + 8 using the algebra tiles?
x = -4
x = -2
x = 2
x = 4
Answer:
x = 2
Step-by-step explanation:
Given
4x + (-4) = -2x + 8 which represents a model of coloured tiles of various lengths (shapes)
Required
Find x
To find x, we'll solve the expression 4x + (-4) = -2x + 8 using the knowledge of algebra.
4x + (-4) = -2x + 8
Open bracket
4x - 4 = -2x + 8
Collect like terms
4x + 2x = 4 + 8
Perform addition arithmetic operation on both sides of the equation
6x = 12
Multiply both sides by ⅙
⅙ * 6x = ⅙ * 12
x = 2
Hence, the value of x that satisfies the expression 4x + (-4) = -2x + 8 is 2
A substance is followed by the symbol (1) in a chemical equation. What does the symbol represent?
Answer:
one atom of that element
Step-by-step explanation:
For example, F1 means one atom of the element Fluorine
What do you think the message is from the "1936 Nazi Poster" poster?
Answer:
Become the leader of our nation.
Step-by-step explanation:
Like all Nazi propaganda, the 1936 poster suggests that young Germans are highly capable of becoming leaders of the nation. A young man who must be blond, with teeth and a perfect body. It was unconditional for Nazi propagandists to convince young people to support the goals and policies of the political party.
On the other hand, the leaders of the Nazi youths sought to integrate the children into the national Nazi community and prepare them to serve as soldiers in the armed forces or, later, in the SS.
Answer this quickly please!
Lisa started to drive from Boston to Washington, DC, which is 440 miles away, at 8:00 AM. For the first four hours of her trip, Lisa was driving at a speed of 50 mph. What was her average speed during the second part of the trip, if she reached Washington at 4:00 PM?
Answer:
[tex]\bar v = 60\,mph[/tex]
Step-by-step explanation:
The distance travelled by Lisa in the first four hours of her trip is:
[tex]\Delta s = \left(50\,mph)\cdot (4\,h)[/tex]
[tex]\Delta s = 200\,mi[/tex]
The distance remaining and her average speed are, respectively:
[tex]\Delta s_{R} = 440\,mi - 200\,mi[/tex]
[tex]\Delta s_{R} = 240\,mi[/tex]
[tex]\bar v = \frac{240\,mi}{4\,h}[/tex]
[tex]\bar v = 60\,mph[/tex]
Solve 2sin^2x=sinx, if 0
Answer: D. 0, pi/6, pi, 5pi/6, and 2pi
Step-by-step explanation:
Refer to screenshot of Desmos graph below
Question: What are all the exact solutions of [tex]2sin^2x-sinx=0[/tex] for [tex]0\leq x\leq 2\pi[/tex]?
Use the following information to determine your answer: The length of a movie falls on a normal distribution. About 95% of movies fall between 75 minutes and 163 minutes.
What is the value of the standard deviation for average movie length in minutes? Please round to the second decimal place.
Answer:
[tex] 75= 119 -1.96 \sigma[/tex]
[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]
And tha's equivalent to use this formula:
[tex] 163= 119 +1.96 \sigma[/tex]
[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]
Step-by-step explanation:
For this case the 95%of the values are between the following two values:
(75 , 163)
And for this case we know that the variable of interest X "length of a movie" follows a normal distribution:
[tex] X \sim N( \mu, \sigma)[/tex]
We can estimate the true mean with the following formula:
[tex]\mu = \frac{75+163}{2}= 119[/tex]
Now we know that in the normal standard distribution we know that we have 95% of the values between 1.96 deviations from the mean. We can find the value of the deviation with this formula:
[tex] 75= 119 -1.96 \sigma[/tex]
[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]
And tha's equivalent to use this formula:
[tex] 163= 119 +1.96 \sigma[/tex]
[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]
Is 9(3r-4) and 27r- 36 equivalent
Answer:
Yes
Step-by-step explanation:
Using the distributive property...
9(3r-4) = (9*3r)-(9*4) = 27r-36
A jar contains 100 marbles. 3/5 of the marbles are black. What fraction of the marbles are black, using 100 as the denominator?
3/5 are black. To rewrite the fraction with a denominator of 100. Find how many thieves the denominator 5 goes into 100:
100/5 = 20
Multiply both the numerator and denominator by 20:
3/5 = 60/100
MARKING BRAINLIEST!!!!
Answer:
Quadratic formula is what I prefer
Answer:
Taking the square root
Step-by-step explanation:
x^2 + 8 = 72
x^2 = 64
take sqrt of 64
x = 8
June gavyn and Alex share some sweets in the ratio 3:5:4 June gets 39 sweets how many sweets are there altogether?
Answer:
146
Step-by-step explanation:
j=3 13 = 39
g=5 13 = 65
a=4 13 = 42
Answer:
156 sweets
Step-by-step explanation:
3+4+5=12
12/12 x 39 x 12/3=156 sweets
2. x + 12 =23
3. X-6 = 13
4. X-9 = 14
5. 2x = 12
6. 3x = 30
Answer:
2. x = 11
3. x = 19
4. x = 23
5. x = 6
6. x = 10
Step-by-step explanation:
2. x + 12 =23
x = 23 - 12
x = 11
3. x - 6 = 13
x = 13 + 6
x = 19
4. x - 9 = 14
x = 14 + 9
x = 23
5. 2x = 12
x = 12/2
x = 6
6. 3x = 30
x = 30/3
x = 10
An item costs n dollars. If the price of the item increases by 15%, the new price can be represented by the expression n + 0.15n. Which expression can also represent the new price?
a. 0.15n
b. n + 1.15
c. 15n
d. None
e. 1.15n
Answer:
d. none
Step-by-step explanation:
Three points, Q,R and S, lie on the same line such as R lies between Q and S . Find QS of RS = 19 an QR =32
Answer:
QS=51
Step-by-step explanation:
It was given that RS = 19 and QR =32
QS=x
Q-R was measured and found to be 32
R-S was measured and found to be 19
Q-S will be the sum of Q-R and R-S which is 32+19= 51
QS=51
Answer:
51
Step-by-step explanation:
I took the test and it was correct :)
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not a question...and scribbles.
Find the missing factor (6 + 3) + 5 = (3 × _?_ ) + 5
Answer:
(6+3)+5=(3x?)+5
9+5=(3×3)+5
14=9+5
14=14
so,the missing factor is 3.
Please Help.... 50 points.
Answer:
94%
Step-by-step explanation:
We need to look at the graph. Olive wants the probability that 20 or more of the 50 babies were female. Looking at the graph, the x-axis is "number of females born out of 50 babies". We want to find the sum of all the ones that are at least 20, or 20 and above.
The numbers above the bars represents how many of each case there are. Above the bar labelled 20, there is the number 11, and so on. So, our sum is:
11 + 17 + 14 + 23 + 16 + 29 + 16 + 23 + 14 + 6 + 9 + 3 + 1 + 2 + 1 + 1 + 1 = 187
In total, there are 200 cases, so our probability is 187 / 200 = 93.5% ≈ 94%.
The answer is thus A.
Step-by-step explanation:
Step 1: Count up how many babies are more than 20
[tex]11 + 17 + 14 + 23+16+29+16+23+14+6+9+3+1+2+1+1+1[/tex]
[tex]187[/tex]
[tex]187 / 200[/tex] ← Will give us percentage of the probability that 20 or more of the 50 babies were born female.
0.935 * 100
93.5%
Answer: Option A, 94%
Answer with explanation
I will and rate on the feedback.
Will mark brainliest too
Answer: 6.6
Step-by-step explanation:
We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.
First triangle:
a = 6
b = 8
c = ?
Use pythagorean's theorem
[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]
[tex]c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10[/tex]
This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.
[tex]c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}[/tex]
[tex]b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6[/tex]
United Express, a nationwide package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $ 25 $25 for shipping a 7 7-pound package and $ 55 $55 for shipping a 22 22-pound package. Find the base price and the surcharge for each additional pound. Round answers to the nearest thousandth (to three decimal places).
Answer:
Base price: $13.
Surcharge: $2 per additional pound.
Step-by-step explanation:
The base price can be considered a constant, while the surcharge is a function of the additional weight of the package, over 1 pound.
Then, we can model this as a linear function, with additional weight as the independent variable.
[tex]f(x)=b+sx[/tex]
being b: base price, and s: surcharge for each additional pound.
The 7-pound package cost $25. The additional weigth in this case is 7-1=6 pounds.
The 22-pound package cost $55. The additional weigth is 21 pounds.
So we have the first point (6, 25):
[tex]f(6)=b+s(6)=25\\\\b=25-6s[/tex]
Then, for the second point (21, 55) we have:
[tex]b=25-6s\\\\f(21)=(25-6s)+s(21)=55\\\\25+(21-6)s=55\\\\15s=55-25=30\\\\s=30/15=2\\\\\\b=25-6(2)=25-12=13[/tex]
Then, the prices are:
Base price: $13.
Surcharge: $2 per additional pound.
If one zero is irrational, the other zero is
Answer:
rational
Step-by-step explanation:
The correct statement is:
c. The other zero can be either rational or irrational.
A quadratic equation with integer coefficients can have two distinct zeros, and if one of the zeros is irrational, the other zero can be either rational or irrational.
The nature of the zeros depends on the specific values of the coefficients in the quadratic equation.
A quadratic equation with integer coefficients can be written in the form: [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are integers.
The solutions to this equation can be found using the quadratic formula:
[tex]\mathrm x = \frac{\mathrm{-b}\pm \sqrt{\mathrm b^2-4\mathrm a \mathrm c} }{2 \mathrm a}[/tex]
If one zero is irrational, it means that one of the solutions obtained from the quadratic formula is an irrational number.
However, the other solution can still be either rational or irrational.
The discriminant, [tex]b^2 - 4ac[/tex], determines the nature of the solutions.
If the discriminant is a perfect square, both solutions will be rational.
If the discriminant is not a perfect square, one solution will be irrational, and the other may be either rational or irrational.
Therefore, it is possible for the other zero to be rational or irrational, depending on the specific values of a, b, and c in the quadratic equation.
Thus, option (c) is the correct answer.
Learn more about quadratic equation click;
https://brainly.com/question/30098550
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Complete question =
Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero?
a. The other zero must be rational.
b. The other zero must be irrational.
c. The other zero can be either rational or irrational.
d. The zero must be non-real.
Complete the equation with a number that makes the expression on the right side of the equal sign equivalent to the expression on the left side 5x - 2.5 + 6x - 3 = ______ (2x - 1)
Answer:
5.5
Step-by-step explanation:
5x-2.5+6x-3=_____(2x-1)
11x-5.5=5.5(2x-1)
11x-5.5=11x-5.5
Answer:
5.5
Step-by-step explanation:
ramon has an employer that offers a generours 401k returement plan roman is allowed to deduct up to 10% from his paycheck to go directly into his retirement account and his emplyer will pay $0.75 for every $1.00 that roman contributes if he contributes 10% of his $80,000 annual gross salary to his 401k how much will actually be going into the retirement account each year ?
Answer:
14000
Step-by-step explanation:
A year he contributes :10/100 × 80000= 8000
Then his employer pays 0.75 × 8000= 6000
The total money contributed to is
401k is = 8000 + 6000 = 14000