Answer:
64 square inches
Step-by-step explanation:
The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.
Each cupcake is 2 inches, so the base is 8 inches by 8 inches. Therefore, the area is 64 square inches.
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.
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
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
Need some help with this .
George and Samantha both applied for a personal loan at Westside Bank. George has a credit score of 650. Samantha has a credit score of 520. The bank approved George’s loan application at 5.6% interest. Samantha was approved for the same loan amount, but, because of her lower credit rating, the interest charged on Samantha’s loan is 3 percentage points higher than the interest rate on George’s loan. What interest rate does Samantha pay to the bank?
A. 8.6%
B. 5.9%
C. 3.0%
D. 2.6%
Option A
Interest rate paid by Samantha to bank is 8.6 %
Solution:
Given that George has a credit score of 650
Samantha has a credit score of 520
The bank approved George’s loan application at 5.6% interest
To find: Interest rate paid by samantha to the bank
From given information in question,
Interest charged on Samantha’s loan is 3 percentage points higher than the interest rate on George’s loan
Thus we get,
Interest charged on Samantha’s loan = 3 percentage points higher than the interest rate on George’s loan
Interest charged on Samantha’s loan = 3 % higher than the interest rate on George’s loan
Interest charged on Samantha’s loan = 3 % + interest rate on George’s loan
Thus substituting the given George’s loan application at 5.6% interest,
Interest charged on Samantha’s loan = 3 % + 5.6 % = 8.6 %
Thus interest rate paid by samantha to bank is 8.6 %
Final answer:
Option A: 8.6%
Samantha will pay an interest rate of 8.6% on her loan from Westside Bank, which is 3 percentage points higher than George's rate of 5.6% due to her lower credit score.
Explanation:
The question involves calculating the interest rate Samantha will pay to the bank for a personal loan.
Given that George has a credit score of 650 and was approved for a loan at 5.6% interest, and Samantha has a lower credit score of 520, her interest rate will be 3 percentage points higher than George's.
To find Samantha's interest rate, we simply add 3 percentage points to George's rate of 5.6%.
Samantha's interest rate = George's interest rate + 3%
Samantha's interest rate = 5.6% + 3%
Samantha's interest rate = 8.6%
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.
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
What is an equation of the parabola with vertex at the origin and focus (-5,0)?
The equation of parabola is expressed as: y² = -20x
What is the equation of the parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.
The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given, vertex = (0, 0)
Focus = (-5, 0)
We have to find the equation of the parabola.
The equation is of the form y = -ax²
Directrix x = 5.
As every point on parabola is equidistant from focus and directrix, the equation will be
y² + (x + 5)² = (x - 5)²
y² + x² + 10x + 25 = x² - 10x + 25
y² = - 10x - 10x
y² = -20x
Therefore, the equation of parabola is y² = -20x
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).
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.
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]
Delete the ribbon is 3/4 meter Sunday needs pieces measuring 1/3 meter for in our project what is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon
Answer:the greatest number of pieces that can be cut is 2
Step-by-step explanation:
The total length of ribbon available is 3/4 meter. Sunday needs pieces measuring 1/3 meter for their project. This means that each length needed would be exactly 1/3 meter.
The number of pieces measuring 1/3 meter that can be cut from the ribbon would be
(3/4)/(1/3) = 3/4×3/1 = 9/4 = 2.25
Since the length needed is exactly 1/3 meter, the greatest number of pieces that can be cut will be 2
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
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.
Learn more about Area calculation here:https://brainly.com/question/32024069
#SPJ3
Pls help me thank you !!
I think 68 or56
It can't be 34 that would be less, 146 would be over quarter
Good evening ,
Answer:
measure arc AB = 68°
Step-by-step explanation:
measure arc AB = 2×(m∠AXB) = 2×(34) = 68°.
:)
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]
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
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]
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!
Find the product of (x-7)^2 and explain how it demonstrates the closure property of multiplication
A. X^2-14x+49; is a polynomial
B. X^2-14x+49; may or may not be a polynomial
C. X^2-49; is a polynomial
D. X^2-49; may or may not be a polynomial
A. x²-14x+49; is a polynomial
Step-by-step explanation:
(x-7)² can be written as (x-7)(x-7)
Expanding the expression
x(x-7)-7(x-7)
x²-7x-7x+49
x²-14x+49 ⇒⇒A quadratic function, which is a polynomial of degree 2
This function demonstrates the closer property of multiplication in that the change in order of multiplication does not change the product. This is called commutative property.
(x-7)(x-7)
-7(x-7)+x(x-7)
-7x+49+x²-7x
x²-14x+49
Learn More
Polynomials :https://brainly.com/question/9601478
Keywords : product, closure property of multiplication,
#LearnwithBrainly
Answer:
A is correct
Step-by-step explanation:
I took the test and got it right
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]
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.
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?
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 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.
Raquel measured milk with a 1/2-cup measuring cup. She filled the cup 5 times and poured each 1/2-cup of milk in a bowl. How much milk did Raquel pour into the bowl?
Answer:
2 1/2 cups
Step-by-step explanation:
5 × (1/2 cup) = 5/2 cup = 2 1/2 cup
__
Or, you can add them up. You know from your study of fractions that two half-cups make 1 cup.
(1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup)
= ((1/2 cup) +(1/2 cup)) +((1/2 cup) +(1/2 cup)) +(1/2 cup)
= (1 cup) + (1 cup) + (1/2 cup)
= (2 cup) + (1/2 cup)
= 2 1/2 cup
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.
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.
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