Answer:
25%.
Step-by-step explanation:
We have been given that at the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed.
We are also told that 1/3 of the roses were short-stemmed.
[tex]\text{Short-stemmed roses}=120\times \frac{1}{3}=40[/tex]
Since 20 of those were white and 15 of which were pink, so short stemmed red roses would be [tex]40-(20+15)=40-35=5[/tex].
Now, we will find number of long-stemmed roses by subtracting number of short-stemmed roses from total roses as:
[tex]\text{Long-stemmed roses}=120-40=80[/tex]
We are also told that none of the long-stemmed roses were white, so total number of white roses would be [tex]20+0=20[/tex].
Let p represent the number of total pink roses.
Now, total number of red roses would be total roses (120) minus total pink roses (p) minus total white roses (20).
[tex]\text{Total red roses}=120-p-20[/tex]
[tex]\text{Total red roses}=100-p[/tex]
We have been given that the percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. We can represent this information in an equation as:
[tex]\frac{\text{Short-stemmed pink roses}}{\text{Total pink roses}}=\frac{\text{Short-stemmed red roses}}{\text{Total red roses}}[/tex]
[tex]\frac{15}{p}=\frac{5}{100-p}[/tex]
Let us solve for p by cross-multiplication:
[tex]1500-15p=5p[/tex]
[tex]1500-15p+15p=5p+15p[/tex]
[tex]1500=20p[/tex]
[tex]20p=1500[/tex]
[tex]\frac{20p}{20}=\frac{1500}{20}[/tex]
[tex]p=75[/tex]
Since total number of pink roses is 75, so total number of red roses would be [tex]100-75=25[/tex].
We already figured it out that 5 roses are short-stemmed, so long-stemmed roses would be [tex]25-5=20[/tex].
Now, we have long stemmed roses is equal to 20 and total long-stemmed roses is equal to 80.
Let us find 20 is what percent of 80.
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{20}{80}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{1}{4}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=25[/tex]
Therefore, 25% of the long-stemmed roses were red.
When abby reaches age of 55, she will deposit $50,000 to fund an annuity with the Dallas cowboys insurance company. The money will be invested at 8% each year, compounded semiannually. She is ro draw payments until she reaches age 65. What is the amount of each payment?
Answer:
The Amount draw from the account after 10 years is $109,555 .
Step-by-step explanation:
Given as :
The principal deposited in account = p = $50,000
The rate of interest = 8% semiannually
The time period for the amount will be in account = t = 10 years
Let The Amount draw from the account after 10 years = $A
Now, From Compound Interest method
Amount = principal × [tex](1+\dfrac{\texrm rate}{2\times 100})^{\textrm 2\times time}[/tex]
A = p × [tex](1+\dfrac{\texrm r}{2\times 100})^{\textrm 2\times t}[/tex]
Or, A = $50,000 × [tex](1+\dfrac{\texrm 8}{2\times 100})^{\textrm 2\times 10}[/tex]
Or, A = $50,000 × [tex](1.04)^{20}[/tex]
Or, A = $50,000 × 2.1911
Or, A = $109,555
So, The Amount draw from the account after 10 years = A = $109,555
Hence,The Amount draw from the account after 10 years is $109,555 . Answer
Given the perimeter of the given shape, find the length of each side of the object.
1) A triangle where the perimeter is 25 inches. The length of the sides are 2w+1, 3w and 3w.
Answer:
The length of each side is 17 in, 24 in, 24 in.
Step-by-step explanation:
Given,
Perimeter of the triangle = [tex]25\ in[/tex]
Length of 1st side = [tex]2w+1[/tex]
Length of 2nd side = [tex]3w[/tex]
Length of 3rd side = [tex]3w[/tex]
The perimeter of a triangle is equal to the sum of the length of all the three sides of the triangle.
Perimeter of the triangle = Length of 1st side + Length of 2nd side + Length of 3rd side
Now substituting the given values, we get;
[tex]2w+1+3w+3w=25\\\\8w+1=25\\\\8w=25-1\\\\8w=24\\\\w=\frac{24}{8}=3[/tex]
Now we have the value of w so we can calculate the length of each side.
Length of 1st side = [tex]2w+1=2\times8+1=16+1=17\ in[/tex]
Length of 2nd side = [tex]3w=3\times8=24\ in[/tex]
Length of 3rd side = [tex]3w=3\times8=24\ in[/tex]
Thus the length of each side is 17 in, 24 in, 24 in.
At the city museumy child admission is and admission is $9.30. On Monday four times as many adult tickets as child tickets were sold for a total of sales of $1548.00 . How many child tickets were sold that day.
Answer:
The number of child tickets sold was 36
Step-by-step explanation:
The complete question is
At the city museum, child admission is $5.80 and adult admission is $9.30. On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1548.00. How many child tickets were sold that day?
Let
x ----> the number of child tickets sold
y ----> the number of adult tickets sold
we know that
[tex]5.80x+9.30y=1,548.00[/tex] ---> equation A
[tex]y=4x[/tex] ----> equation B
Solve by substitution
Substitute equation B in equation A
[tex]5.80x+9.30(4x)=1,548.00[/tex]
solve for x
[tex]5.80x+37.2x=1,548.00[/tex]
[tex]43x=1,548.00[/tex]
[tex]x=36[/tex]
therefore
The number of child tickets sold was 36
Craig has a box of chocolates to share when his friends. The box has 5 rows of chocolate with 20 chocolates in row. Craig and his friends eat 64 chocolates. How much did they eat? Show this as an decimal.
Answer:
0.64
Step-by-step explanation:
Given: Craig has a box of chocolate with 5 rows in it.
Each row has 20 chocolate.
Craig and his friends eat 64 chocolate.
As given, we understand that there is box of chocolate with 5 rows and each row have 20 chocolate, therefore we can find total number of chocolate.
Total number of chocolate=[tex]5\ rows \times 20\ chocolates = 100\ chocolates[/tex]
∴ Total number of chocolates in box= 100.
Now, we know craig and his friends eat 64 chocolate.
∴ To find decimal of number chocolate eaten out of 100 chocolate, we need to put numbers in fraction first then convert it in decimal.
Number of chocolate ate by craig and his friends is [tex]\frac{64}{100} = 0.64[/tex]
∴ Craig and his friends eat 0.64 chocolates.
In the company Educational Solutions, the ratio of the employees using a laptop computer to those not using one was 1:3 in the year 2005. In 2006, the number of employees using a laptop as well as those not using it doubled. What was the ratio of the employees using a laptop to those not using one in 2006?
Answer:
the answer is 1:12
Step-by-step explanation:
hope it helps!
Mrs. Mary Moolah invested $20,000 in
two different types of bonds. The first
type paid a 5% interest rate, and the
second paid an 8% rate. Lif Mrs. Moolah's
combined profit from both investments
was $1,150, how much did she invest at
the 5% rate?
Answer: the amount of money invested at the 5% rate is $15000
Step-by-step explanation:
Let x represent the amount of money invested at the rate of 5%.
Let y represent the amount of money invested at the rate of 8%.
Mrs. Mary Moolah invested $20,000 in two different types of bonds. This means that
x + y = 20000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time
Considering the investment at the rate of 5%,
P = x
R = 5
T = 1
I = (x × 5 × 1)/100 = 0.05x
Considering the investment at the rate of 8%,
P = y
R = 8
T = 1
I = (y × 8 × 1)/100 = 0.08y
If Mrs. Moolah's combined profit from both investments was $1,150, it means that
0.05x + 0.08y = 1150 - - - - - -1
Substituting x = 20000 - y into equation 1, it becomes
0.05(20000 - y) + 0.08y = 1150
1000 - 0.05y + 0.08y = 1150
- 0.05y + 0.08y = 1150 - 1000
0.03y = 150
y = 150/0.03 = 5000
Substituting y = 5000 into x = 20000 - y, it becomes
x = 20000 - 5000
x = 15000
Assume that a procedure yields a binomial distribution with a trial that is repeated 10 times. Use the binomial probability formula to find the probability of 6 successes given that a single success has a probability of 0.30.
Answer: 0.036756909
Step-by-step explanation:
Formula for Binomial probability distribution.
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
, where x= number of success
n= total trials
p=probability of getting success in each trial.
According to the given information , we have
n= 10 , p= 0.30 and x= 6
Then, the required probability will be :
[tex]P(x=6)=^{10}C_6(0.3)^6(1-0.3)^{10-6}\\\\= \dfrac{10!}{6!(10-6)!}\times(0.3)^6(0.7)^4\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}(0.3)^6(0.7)^4\\\\=(210)(0.000729)(0.2401)=0.036756909[/tex]
Hence, the required provability = 0.036756909
The probability of 6 successes given that a single success has a probability of 0.30 is given by the binomial distribution and P ( A ) = 0.03675 or 3.675 %
Given data ,
To find the probability of exactly 6 successes in 10 trials, with a probability of success (p) equal to 0.30, we can use the binomial probability formula:
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
P(X = k) is the probability of getting exactly k successes,
n is the total number of trials,
k is the number of desired successes,
p is the probability of success for a single trial,
In this case, n = 10, k = 6, and p = 0.30. The binomial coefficient C(n, k) is calculated as:
P(n, k) = n! / (k! * (n - k)!)
Substituting the values into the formula, we have:
P(X = 6) = C(10, 6) x (0.30)⁶ * (1 - 0.30)⁽¹⁰⁻⁶⁾
Calculating the binomial coefficient:
C(10, 6) = 10! / (6! x (10 - 6)!)
= 10! / (6! x 4!)
= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
= 210
Substituting the values into the formula:
P(X = 6) = 210 x (0.30)⁶ (0.70)⁴
P ( X = 6 ) = P ( A ) = 210 ( 0.000729 ) ( 0.2401 )
P ( A ) = 0.036756909
Therefore, the probability of getting exactly 6 successes in 10 trials, with a probability of success of 0.30, is approximately 0.03675 or 3.675 %
To learn more about binomial distribution click :
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Need help with two questions I am not good with this
Answer:
Part 12) [tex]Center\ (2,-3),r=2\ units, (x-2)^2+(y+3)^2=4[/tex]
Part 13) [tex]m\angle ABC=47^o[/tex]
Step-by-step explanation:
Part 12) we know that
The equation of a circle in center-radius form is equal to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
In this problem
Looking at the graph
The center is the [tex]point\ (2,-3)[/tex]
The radius is [tex]r=2\ units[/tex]
substitute in the expression above
[tex](x-2)^2+(y+3)^2=2^2[/tex]
[tex](x-2)^2+(y+3)^2=4[/tex]
Part 13) we know that
The measure of the external angle is the semi-difference of the arcs it covers.
so
[tex]m\angle ABC=\frac{1}{2}[arc\ DE-arc\ AC][/tex]
we have
[tex]arc\ DE=142^o[/tex]
[tex]arc\ AC=48^o[/tex]
[tex]m\angle ABC=\frac{1}{2}[142^o-48^o][/tex]
[tex]m\angle ABC=47^o[/tex]
A cab in NYC charges you $1.25 a mile and a flat fee of $4 to ride in the cab. A cab in Chicago charges you $0.75 a mile but a flat fee of $6 just to get in the cab. If you paid the same amount of money for a cab ride in each city how many miles would the cab have driven you?
Answer:
After 4 miles driven by cab the amount would be same in both cities.
Step-by-step explanation:
Let the number of miles be 'x'.
Given:
In NYC
Flat fee of cab = $4
Per mile charge = $1.25
Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.
Framing in equation form we get;
Total cab charges in NYC = [tex]4+1.25x[/tex]
In Chicago
Flat fee of cab = $6
Per mile charge = $0.75
Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.
Framing in equation form we get;
Total cab charges in Chicago = [tex]6+0.75x[/tex]
Now we need to find number of miles driven so that the amount could same in both cities.
Total cab charges in NYC = Total cab charges in Chicago
[tex]4+1.25x=6+0.75x[/tex]
Combining like terms we get;
[tex]1.25x-0.75x=6-4\\\\0.5x=2[/tex]
using Division Property we will divide both side by 0.5 we get;
[tex]\frac{0.5x}{0.5} =\frac{2}{0.5} \\\\x=4[/tex]
Hence After 4 miles driven by cab the amount would be same in both cities.
You want to invest in a hot dog stand near the ballpark. You have a 0.35 probability that you can turn your current $15,000 into $50,000 and an 0.65 probability that fierce competition will drive you to ruin, losing all your money. If you decide not to enter, you keep your $15,000. Would you enter the market?
Answer:
Step-by-step explanation:
The probability that you can turn your current $15,000 into $50,000. This means that the probability of success is 0.35. In terms of percentage, it is 0.35×100 = 35%
You have a 0.65 probability that fierce competition will drive you to ruin, losing all your money. This means that the probability of failure is 0.65. In terms if percentage, it is 0.65×100 = 65%
Looking at the percentage, entering the market will be too risky so I won't enter market since the chance of failing is very high compared to that of succeeding
Kenneth John makes a deposit at an ATM and receives $75.00 in cash and a receipt for the $872.25 total deposit. He remembers that the checks deposited totaled twice the currency he deposited. He did not deposit any coins. What amount in currency did he deposit? What amount in checks did he deposit?
Answer:
Currency= $291 and check= $581.25.
Step-by-step explanation:
Given: Cash received= $75
Total deposit= $872.25
Lets assume currency deposited be dollar "x"
∴ As given check deposited will be "2x"
Now, calculating amount of currency deposited.
We know that, [tex]currency\ deposit + check\ deposit= \$872.25[/tex]
∴ [tex]x+2x= \$872.25[/tex]
⇒[tex]3x=\$872.25[/tex]
Cross multiplying
∴[tex]x= \$290.75 \approx \$291 \textrm{ as Kenneth John have not deposited any coins}[/tex]
∴ Amount of currency deposited is $291.
Next, computing to get amount deposited through check.
As we know check deposited is double of currency.
Check deposited= [tex]2\times \$291= \$ 582[/tex]
∵ No coins were deposited and there is total deposit is $872.25.
∴ We will consider amount deposited through check is $581.25.
Kenneth John deposited $290.75 in currency and $581.50 in checks.
To determine the amounts of currency and checks deposited by Kenneth John, we will define the variables for clarity. Let C represent the amount in currency deposited and CH represent the amount in checks deposited.
Given:
The total deposit after adding checks and currency is $872.25.
The checks deposited totaled twice the currency deposited (CH = 2C).
We can set up the following equation based on the given information:
[tex]C + CH = 872.25[/tex]
Since CH = 2C, we substitute CH:
[tex]C + 2C = 872.25[/tex]
This simplifies to:
[tex]3C = 872.25[/tex]
Solving for C, we divide both sides of the equation by 3:
[tex]C = \[\frac{872.25}{3} = 290.75[/tex]
Kenneth deposited $290.75 in currency.
Then, we calculate the amount in checks:
[tex]CH = 2 \times 290.75 = 581.50[/tex]
In triangle ABC, the measure of angle B is 60 more than A. The measure of angle C is eight times the measure of A. If x represents the measure of angle A, set up and solve an equation to find the measure of angle A.
Answer: the measure of angle A is 12 degrees
Step-by-step explanation:
Let x represent the measure of angle A.
Let y represent the measure of angle B.
Let z represent the measure of angle C.
In triangle ABC, the measure of angle B is 60 more than A. This means that
y = x + 60
The measure of angle C is eight times the measure of A. This means that
z = 8x
Also, the sum of the angles in a triangle is 180 degrees. Therefore
x + y + z = 180 - - - - - - - - - 1
Substituting y = x + 60 and z = 8x into equation 1, it becomes
x + x + 60 + 8x = 180
10x + 60 = 180
10x = 180 - 60 = 120
x = 120/10 = 12
Answer:
Step-by-step explanation:
measure of A=x
∠C=8x
∠B=x+60
in a triangle sum of angles=180°
x+8x+x+60=180
10x=120
x=12
m∠A=12°
Denzel earned money after school delivering newspapers and doing yardwork. He put - of this month's earnings into his savings. He took the rest to spend at the amusement park. He spent of this amount on popcorn and of it on rides. What fraction of his amusement park money did he spend on rides and popcorn?
Denzel took 1/40 of his earnings to the park but did not spend it on rides or popcorn.
Let's break down the information provided step by step to find the fraction of Denzel's earnings that he took to the park but did not spend on rides or popcorn.
Denzel put 1/2 of his earnings into savings. This means he kept 1/2 as his spending money for the amusement park.
Denzel spent 1/5 of the remaining amount on popcorn. This means he spent 1/5 * 1/2 = 1/10 of his earnings on popcorn.
Denzel also spent 3/4 of the remaining amount on rides. This means he spent 3/4 * 1/2 = 3/8 of his earnings on rides.
To find the fraction of his earnings that he took to the park but did not spend on rides or popcorn, we need to subtract the fractions spent on rides and popcorn from the fraction he took to the park.
Fraction taken to the park but not spent on rides or popcorn = 1/2 - (1/10 + 3/8)
To subtract fractions, we need a common denominator. The least common multiple of 10 and 8 is 40.
Converting the fractions to have a common denominator:
1/2 - (1/10 + 3/8) = 20/40 - (4/40 + 15/40) = 20/40 - 19/40 = 1/40
Therefore, Denzel took 1/40 of his earnings to the park but did not spend it on rides or popcorn.
Question: Denzel earned money after school. He put 1/2 of this month's earnings into savings. He took the rest to spend at the amusement park. He spent 1/5 of this amount on popcorn and 3/4 of it on rides. What fraction of his earnings did he take to the park but not spend on rides or popcorn?
True or False:The following pair of ratios forms a proportions.3/2 and 18/8
Answer:
Correct answer: False
Step-by-step explanation:
coeff c= 3/2 = 1,5 coeff c₁ = 18/8 = 2,25
c ≠ c₁
God is with you!!!
Answer: False
Step-by-step explanation: When we are asked to determine whether two ratios form a proportion, what we are really being asked to do is to determine whether the ratios are equal because if the ratios are equal, then we know they form a proportion.
So in this problem, we need to determine whether 3/2 = 18/8. The easiest way to determine whether 3/2 = 18/8 is to use cross products. If the cross products are equal, then the ratios are equal.
The cross products for these two ratios are 3 x 8 and 2 x 18.
Since 3 x 8 is 24 and 2 x 18 is 36, we can easily see that 24 ≠ 36 so the cross products are not equal which means that the ratios are not equal and since the ratios are not equal, we know that they do not form a proportion.
So the answer is false. 3/2 and 18/8 do not form a proportion.
a)Find a recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s. b) What are the initial conditions? c) How many ternary strings of length six do not contain two consecutive 0s?
a) The recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s is [tex]\(a_n = 2a_{n-1} + a_{n-2}\).[/tex]
b) The initial conditions for the recurrence relation are [tex]\(a_1 = 3\) and \(a_2 = 9\).[/tex]
c) There are 21 ternary strings of length six that do not contain two consecutive 0s.
Explanation:a) To derive the recurrence relation, consider the possibilities for the last digit in the string. If the last digit is 1 or 2, it doesn't affect the constraint of avoiding consecutive 0s. Hence, for strings of length n that end in 1 or 2, there are[tex]\(a_{n-1}\)[/tex]possibilities. However, if the last digit is 0, the previous digit cannot be 0 to satisfy the constraint. Therefore, for strings of length n that end in 0, there are \(a_{n-2}\) possibilities. This results in the recurrence relation[tex]\(a_n = 2a_{n-1} + a_{n-2}\).[/tex]
b) The initial conditions are established by considering strings of length 1 and 2. For strings of length 1, there are three possibilities (0, 1, or 2). For strings of length 2, there are nine possibilities (00, 01, 02, 10, 11, 12, 20, 21, 22), but among these, 00 is excluded to avoid consecutive 0s, leaving a total of nine valid strings. Therefore, the initial conditions are[tex]\(a_1 = 3\) and \(a_2 = 9\).[/tex]
c) To find the number of ternary strings of length six that do not contain two consecutive 0s, utilize the recurrence relation. Starting from the initial conditions, compute[tex]\(a_6 = 2a_5 + a_4\)[/tex] using the relation, which results in [tex]\(a_6 = 21\).[/tex]
Thus, there are 21 ternary strings of length six that satisfy the condition of not having two consecutive 0s.
"In summary, the recurrence relation [tex]\(a_n = 2a_{n-1} + a_{n-2}\)[/tex]governs the number of ternary strings of length n without consecutive 0s, with initial conditions[tex]\(a_1 = 3\) and \(a_2 = 9\)[/tex]. Computing[tex]\(a_6\)[/tex]using the relation yields 21 valid ternary strings of length six that do not contain two consecutive 0s."
The recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s is a_n = 2a_n-1 + 2a_n-2. The initial conditions are a_1 = 3 and a_2 = 8. Using these, we calculate that there are 448 such ternary strings of length six.
Ternary Strings without Consecutive 0s
Let's define a ternary string as a string composed of the digits 0, 1, and 2. We need to find a recurrence relation for the number of such strings of length n that do not contain two consecutive 0s.
Part (a)
Let a_n represent the number of ternary strings of length n that do not contain consecutive 0s. Consider the possibilities for the first digit of the string:
If the first digit is 1 or 2, the remaining (n-1) digits can be any string of length (n-1) that does not contain consecutive 0s.If the first digit is 0, the second digit must be 1 or 2 (to avoid two consecutive 0s). The remaining (n-2) digits can be any string of length (n-2) that does not contain consecutive 0s.Thus, we have the recurrence relation: a_n = 2a_{n-1} + 2a_{n-2}
Part (b)
The initial conditions can be determined as follows:
a_1: There are three ternary strings of length 1 (0, 1, 2). Therefore, a_1 = 3.a_2: We need to count the ternary strings of length 2 that do not contain two consecutive 0s. These are 01, 02, 10, 11, 12, 20, 21, 22. Therefore, a_2 = 8.Part (c)
Using the recurrence relation and initial conditions:
a_3 = 2a_2 + 2a_1 = 2(8) + 2(3) = 22a_4 = 2a_3 + 2a_2 = 2(22) + 2(8) = 60a_5 = 2a_4 + 2a_3 = 2(60) + 2(22) = 164a_6 = 2a_5 + 2a_4 = 2(164) + 2(60) = 448Therefore, the number of ternary strings of length six that do not contain two consecutive 0s is 448.
Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. How much interest will he have earnt after 3 years?
Answer: her interest in 3 years is $45
Step-by-step explanation:
For simple interest, the principal is not compounded. The interest is only on the original capital. The formula for simple interest is expressed as
I = PRT/100
Where
I represents the interest on the principal
P represents the initial amount
R represents the interest rate.
T represents the time in years.
From the information given
P = $300
R = 5%
T = 3 years
I = 300×5×3)/100
I = 4500/100 = 45
A strip mall generates $215,000 in effective rental income and $3,000 in other income. The same mall has $102,000 in operating expenses and $15,000 as reserves. What is the net operating income ofthe strip mall?
A. $113,000
B. $99,000
C. $101,000
D. $116,000
Answer: $116,000
Step-by-step explanation:
The net operating income will be the operation profit after deducting the expenses from the accrued revenue (reserve exclusive)
The revenue generated are $215,000 + $3,000
= $218,000
Expenses incurred;
$102,000
The net operating income = $218,000 - $102,000
= $116,000
Note that reserves is not used in business operation. Therefore it cannot be regarded either as revenue or expenses.
Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?A) (x – y)/(x + y)B) x/(y – x)C) (x + y)/(xy)D) y/(x – y)E) y/(x + y)
Answer:
[tex]\frac{y}{x+y}[/tex]
Step-by-step explanation:
The required answer is the rate at which Machine A works when the two machines are combined.
Note: the rate of doing work is express as
[tex]rate=\frac{1}{time taken} \\[/tex]
Hence we can conclude that Machine A working rate is
[tex]machine A=\frac{1}{x} \\[/tex] and machine B working rate is
[tex]machine B=\frac{1}{y} \\[/tex]
When the two machine works together, the effective working rate is
[tex]\frac{1}{x}+\frac{1}{y}\\\frac{xy}{x+y}\\[/tex]
The fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A
Hence the fraction of work done by A is expressed as
[tex]\frac{1}{x}*combine working rate[/tex]
[tex]\frac{1}{x}*\frac{xy}{x+y}\\\frac{y}{x+y} \\[/tex]
Hence the fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A is [tex]\frac{y}{x+y} \\[/tex]
Mr Thomson wants to protect his garage by installing a flood barrier.He connects two barriers side by side.Each barrier is 9 feet long by 2 feet high.What is the combined area of the barriers?
Answer:
36 square feet
Step-by-step explanation:
The area of one barrier is the product of the given dimensions:
(9 ft)(2 ft) = 18 ft²
Two such barriers will have twice the area: 36 ft².
The combined area of the two barriers is calculated by multiplying the length by the height for each barrier to get an area for each one, and then those two areas are added together. Each barrier has an area of 18 square feet, so the total combined area is 36 square feet.
Explanation:The question is asking for the combined area of two barriers, each being 9 feet long and 2 feet high. In order to find this, we must multiply the length by the height for each barrier, and then add these two areas together. The calculation would look like this:
Area of each barrier = Length x Height = 9 ft x 2 ft = 18 square feet
Now, since there are two barriers:
Combined Area = 2 x Area of each barrier = 2 x 18 square feet = 36 square feet
Therefore, the combined area of the two barriers is 36 square feet.
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Some friends are making cookies for a bake sale. In all they need 6 cups of flour however they only have a 1/4 measuring cup. How many time will they need to fill the measuring cup
Answer:
24 times
Step-by-step explanation:
Given:
Number of cups required = 6 cups
Measuring cup capacity = [tex]\frac{1}{4}=0.25[/tex] of a cup.
Now, each time the measuring cup fills 0.25 of a cup.
So, we use unitary method to find the number of times the measuring cup has to be used to get a total of 6 cups.
∵ 0.25 cups = 1 time the measuring cup being used.
∴ 1 cup = [tex]\frac{1}{0.25}=4[/tex] times the measuring cup being used.
So, 6 cups = [tex]4\times 6=24[/tex] times the measuring cup being used.
Hence, the number of times the measuring cup has to be used to get 6 cups of flour is 24 times.
When the denominator of \dfrac{2}{\sqrt{3}} 3 2 start fraction, 2, divided by, square root of, 3, end square root, end fraction is rationalized, it becomes \dfrac{2k}{3} 3 2k start fraction, 2, k, divided by, 3, end fraction. Find kkk
Answer:
Step-by-step explanation:
k = 6
To find the value of k, rationalize the denominator of 2/√3, and compare it with 2k/3 to find k = √3.
To rationalize the denominator of the fraction 2/√3, we need to make the denominator a rational number. We can do this by multiplying both the numerator and the denominator by √3.
Multiply the numerator and the denominator by √3:[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3} = \frac{2\sqrt3}{3}[/tex]So, after rationalizing, the fraction becomes 2√3/3. According to the problem statement, this is equivalent to 2k/3.
Therefore, we can equate 2k to 2√3:
2k = 2√3
k = √3
So, the value of k is √3.
The complete question is
When the denominator of 2/√3 is rationalized ,it becomes 2k/3. Find k
slader An electronics company is planning to introduce a new camera phone. The company commissions a marketing report for each new product that predicts either the success or failure of the product. Of new products introduced by the company, 60% have been successes. Furthermore, 70% of their successful products were predicted top be successes, while 40% of failed products were predicted to be successes. Find the probability that this new camera phone will be successful if its success has been predicted.
Answer: Our required probability is 0.7241.
Step-by-step explanation:
Since we have given that
Probability that new product have been successes P(S) = 60%
Probability that new product have not been successes P(F) = 40%
Probability that their successful products were predicted to be successes = P(A|S)=70%
Probability that their failed products were predicted to be successes =P(A|F) = 40%
So, Probability that this new camera phone will be successful if its success has been predicted is given by
[tex]P(S|A)=\dfrac{P(S).P(A|S)}{P(S).P(A|S)+P(F).P(A|F)}\\\\P(S|A)=\dfrac{0.7\times 0.6}{0.7\times 0.6+0.4\times 0.4}\\\\P(S|A)=0.7241[/tex]
Hence, our required probability is 0.7241.
John is 4 years older than Becky, and John’s and Becky’s combined ages is 58. How old are Becky and John?A. Becky is 26; John is 32 B. Becky is 26; John is 30 C. Becky is 27; John is 31 D. Becky is 25; John is 29
Answer:
Answer C: Becky is 27; John is 31
Step-by-step explanation:
1. John is 4 years older than Becky--27(Becky's age)+ 4=31(John's age)
2. Sum of their ages is 58--27(Becky's age)+31(John's age)=58
So, the correct answer is Answer C.
Answer:
C. Becky is 27; John is 31
What is the equation, in standard form, of a parabola that models the values in the table?
Using the values in the table you can easily use the provided x-values to plug into any equation to get a corresponding f(x) value. When applying this to the 4 functions, we see that only the second answer choice will give the exact same outputs when the inputs are plugged in from the table.
[tex]4x^2+3x-6[/tex]
[tex]x=-2\\f(-2)=4(-2)^2+3(-2)-6\\f(-2)=4[/tex]
[tex]x=0\\f(0)=4(0)^2+3(0)-6\\f(0)=-6[/tex]
[tex]x=4\\f(4)=4(4)^2+3(4)-6\\f(4)=70[/tex]
The coordinates of the endpoints of line AB are graphed in the standard (x, y) coordinate plane at (10, 14) and (4, -2). What is the y-coordinate of the midpoint of line AB?
y coordinate of midpoint of line AB is 6
Solution:
Given that endpoints of line AB is (10, 14) and (4, -2)
To find: y-coordinate of the midpoint of line AB
The midpoint of line AB is given as:
For a containing [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex] the midpoint is given as:
[tex]M(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this question,
[tex]\left(x_{1}, y_{1}\right)=(10,14) \text { and }\left(x_{2}, y_{2}\right)=(4,-2)[/tex]
So midpoint is:
[tex]\begin{aligned}&M(x, y)=\left(\frac{10+4}{2}, \frac{14-2}{2}\right)\\\\&M(x, y)=\left(\frac{14}{2}, \frac{12}{2}\right)\\\\&M(x, y)=(7,6)\end{aligned}[/tex]
Therefore y coordinate of midpoint of line AB is 6
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is
4.4 MB. Yesterday, there were 1310 downloads of the song, for a total download size of 4752 MB. How many downloads of the standard version were there?
Answer:
There were 440 Standard version of songs downloaded in Web music store.
Step-by-step explanation:
Given,
Total number of songs downloaded = 1310
Total size of the downloaded songs = 4752 MB
Size of standard version of song = 2.1 MB
Size of high quality version of song = 4.4 MB
Solution,
Let the number of standard version of song be 'x'.
And also let the number of high quality version of song be 'y'.
Now, total number of songs is the sum of total number of standard version of song and total number of high quality version of song.
On framing the above sentence in equation form, we get;
[tex]x+y=1310\ \ \ \ \ equation\ 1[/tex]
Now, Total size of the downloaded songs is the sum of total number of standard version of song multiplied with size of standard version of song and total number of high quality version of song multiplied with size of high quality version of song.
On framing the above sentence in equation form, we get;
[tex]2.1x+4.4y=4752[/tex]
Multiplying with 10 on both side, we get;
[tex]10(2.1x+4.4y)=4752\times10\\\\21x+44y=47520\ \ \ \ equation\ 2[/tex]
Now multiplying equation 1 by 21, we get;
[tex]21(x+y)=1310\times21`\\\\21x+21y=27510\ \ \ \ equation\ 3[/tex]
Now subtract equation 3 from equation 2, we get;
[tex](21x+44y)-(21x+21y)=47520-27510\\\\21x+44y-21x-21y=20010\\\\23y=20010\\\\y=\frac{20010}{23}\\\\y=870[/tex]
On substituting the value of y in equation 1, we get the value of x;
[tex]x+y=1310\\\\x+870=1310\\\\x=1310-870=440[/tex]
Hence There were 440 Standard version of songs downloaded in Web music store.
Need some help with this .
Three different die are rolled __ probability that exactly to roll tthe same number.
Answer: Our required probability is [tex]\dfrac{1}{36}[/tex]
Step-by-step explanation:
Since we have given that
Total number of outcomes in single die = 6
So, total number of outcomes if three different die = [tex]6^3=216[/tex]
Number of favourable outcome i.e. exactly roll the same number = (1,1,1), (2,2,2) (3,3,3) (4,4,4) (5,5,5), (6,6,6) = 6
So, Probability of getting exactly roll the same number is given by
[tex]\dfrac{\text{number of favourable outcome}}{\text{Number of total outcomes}}\\\\=\dfrac{6}{216}\\\\=\dfrac{1}{36}[/tex]
Hence, our required probability is [tex]\dfrac{1}{36}[/tex]
Tyrone’s financial goal is to create an emergency fund. To make Tyrone’s financial goal specific, he could give himself a . To make his goal timely, he could give himself a .
Answer:
Goal amount of $10,000
Deadline of next year
Step-by-step explanation:
Tyrone can make his financial goal ‘specific’ by deciding on a target amount for his emergency fund. He can make it 'timely' by assigning a deadline by which to save that amount.
Explanation:To make Tyrone's financial goal specific, he could give himself a target amount to save for the emergency fund. This could be a fixed sum, like $1000, or a figure based on monthly expenses, like saving for 6 months' worth of living expenses. This clarity can help him to plan and track his progress.
To make his goal timely, he could give himself a deadline by which he wants to achieve this goal. For example, he might aim to save his specified amount within a year or two. The timetable can provide added motivation to adhere to a budget and save consistently.
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Rewrite with only sin x and cos x.
cos 3x
Answer:
cos(3x) --> cos³(x) - 3sin²(x)cos(x)
Step-by-step explanation:
The text in pink are the trig identities I used to convert cos(2x) and sin(2x) into their other equivalent forms.
This question is pretty much asking if you know how to use your trig identities if i understand it correctly.
Final answer:
To rewrite cos 3x using only sin x and cos x, we can use the trigonometric identity: cos 3x = 4(cos x)^3 - 3(cos x). This identity allows us to express cos 3x in terms of cos x. However, if we want to rewrite it using only sin x and cos x, we can use the Pythagorean identity: (cos x)^2 = 1 - (sin x)^2.
Explanation:
To rewrite cos 3x using only sin x and cos x, we can use the trigonometric identity: cos 3x = 4(cos x)^3 - 3(cos x). This identity allows us to express cos 3x in terms of cos x. However, if we want to rewrite it using only sin x and cos x, we can use the Pythagorean identity: (cos x)^2 = 1 - (sin x)^2. So, we can substitute this identity into the previous equation to get: cos 3x = 4(1 - (sin x)^2)^3 - 3(1 - (sin x)^2).