The carrot cakes are the fraction of the cake given by [tex]1 - \frac{6}{7}[/tex] multiplied by [tex]\frac{1}{3}[/tex]
The fraction of the cakes that are carrot cakes is [tex]\underline {\dfrac{1}{21}}[/tex]How are the cakes evaluated as fractions?The fraction of the cake that are chocolate cake = [tex]\dfrac{2}{3}[/tex]
The fraction of the remaining cake that cheesecakes = [tex]\dfrac{6}{7}[/tex]
The rest of the cakes = carrot cakes
Required:
The fraction of the cake that are carrot cakes
Solution:
The fraction of the cakes that are not chocolate cake = [tex]1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}[/tex]
The fraction of the remaining cakes that are cheesecake = [tex]\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}[/tex]
The fraction of the cake that are carrot cake = [tex]\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}[/tex]
The fraction of the cakes that are carrot cake is [tex]\underline{\dfrac{1}{21}}[/tex]Learn more about fractions here:
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Someone help please 15 points no links
Answer:
see explanation
Step-by-step explanation:
A) 1.25x is the equation. 10-5/8-4= 5/4. and so it is 1.25 for the slope.
B) 1.25(-4)= $-5
C) it does not make sense since you cannot have negative bags of candy
Rewrite the set N by listing its elements. Make sure to use the appropriate set notation.
N={z | z is an integer and -3
Answer:
please see the analysis
Step-by-step explanation:
Solution:
the Integer between [tex]-3So [tex]Z=-2 , -1 ,[/tex]
So [tex]P=\left\{-2\middle|-1\right\}[/tex] {write all the value of Z}
How would you turn a fraction into a decimal? Give a detailed explanation
Answer:
The way I learned was by determining the denominator such 7/10 would be 0.7 because 7 is located in the tenths place.
/G/To convert a fraction to a percent, first divide the numerator by the denominator. Then multiply the decimal by 100 .
solve system of equations:
10x + 8y = -10
7x + 10y = 15
Answer:
(x,y)=(-5,5)
Step-by-step explanation:
[tex]10x + 8y = -10\\\underline{7x + 10y = 15}\\-44y=-220\\y=\cfrac{220}{44} \\y=5[/tex]
[tex]10x+8y=-10\\10x+8\times 5=-10\\10x+40=-10\\102=-10-40\\10x=-50\\x=-50/10\\x=-5[/tex]
Hope it helps!
Help!!! Use 1st and 2nd differences to determine if the following table is linear, quadratic or neither.
Given the second difference, the table is quadratic.
What are linear and quadratic equations?A linear function is a function that has a single variable raised to the power of 1. An example is x + 2. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. An example is 2x² + 10x + 25.
What are the first and second differences?First differences:
21 - 11 = 10
35 - 21 = 14
53 - 35 = 18
75 - 53 = 22
Due to the fact that the first difference is not the same, the function is not a linear function.
Second difference:
14 - 10 = 4
18 - 14 = 4
22 - 18 = 4
Due to the fact that the second difference is fairly constant, the function is a quadratic function.
To learn more about linear functions, please check: https://brainly.com/question/26434260
Need Help !!
Question 1 )
If sin θ – cos θ = 0, find the value of sin4 θ + cos4 θ. (2012, 2017D).
Notes ;
Kindly don't spam.
Need Authentic Answer.
Don't copy from other website , Give answer in ur own logic ....
[tex] \huge \mathbb{\green{\fbox{\pink{ANSWER}}}} [/tex]
[tex] \\ \: \: \implies \: sin^{4} \: \theta + cos^{4} \: \theta \rightarrow \blue{ \frac{1}{2} } [/tex]
[tex] \\ \\ \: \large \mathfrak \green{Solution} : [/tex]
[tex] \\ \bf \: Given : [/tex]
[tex] \\
\sf \: \: \bf sin \: \theta - cos \: \theta = 0 [/tex]
[tex] \\ \sf \rightarrow \: sin \: \theta = cos \: \theta [/tex]
[tex] \\ \sf \rightarrow \: \frac{sin \: \theta} {cos \: \theta} = 1 [/tex]
[tex] \\ \sf \rightarrow \: tan \: \theta = 1 [/tex]
[tex] \\ \sf \rightarrow \: tan \: \theta = tan \: 45 \degree [/tex]
[tex] \\ \sf \rightarrow \: \theta = 45 \degree [/tex]
[tex] \\ \\ \therefore \: sin^{4} \: \theta + cos^{4} \: \theta [/tex]
[tex] \\ \sf \rightarrow \: sin^{4} \: 45 \degree + cos^{4} \: 45 \degree [/tex]
[tex] \\ \\
\sf \rightarrow \: (\frac{1}{ \sqrt{2} } ) ^{4} +(\frac{1}{ \sqrt{2} } ) ^{4} [/tex]
[tex] \\ \sf \rightarrow \: ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}} + ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}} [/tex]
[tex] \\ \\
\sf \rightarrow \: \frac{1}{2} × \frac{1}{2} + \frac{1}{2}× \frac{1}{2} [/tex]
[tex] \\ \\ \sf \rightarrow \: \frac{1}{4} + \frac{1}{4} [/tex]
[tex] \\ \\ \sf \rightarrow \: {\cancel \frac{2} {4}}[/tex]
[tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \fbox{\pink {\frac{1}{2}}} [/tex]
The value of [tex]sin^4\theta+cos^4 \theta[/tex] will be [tex]\frac{2}{(\sqrt{2})^4}[/tex]
Trigonometry identityGiven the expression
sin θ – cos θ = 0
This can be simplified further as:
sin θ = cos θ
sin θ/cosθ = cosθ/cosθ
tanθ = 1
θ = arctan(1)
θ = 45 degrees
To evaluate [tex]sin^4\theta+cos^4 \theta[/tex], substitute the value of theta into the expression to have:
[tex]sin^4\theta+cos^4 \theta\\=sin^445+cos^4 45\\=(\frac{1}{\sqrt{2}} )^4+(\frac{1}{\sqrt{2}} )^4\\=2(\frac{1}{(\sqrt{2})^4} )[/tex]
Hence the value of [tex]sin^4\theta+cos^4 \theta[/tex] will be [tex]\frac{2}{(\sqrt{2})^4}[/tex]
Learn more on trigonometry identity here: https://brainly.com/question/7331447
Please help!
Steven borrows $60,000 for school. The intrest rate is 6.5%. He wants to pay off the loan in 12 years. What would be the simple intrest rate?
Answer:
i think it is $106,800.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.5%/100 = 0.065 per year.
Solving our equation:
A = 60000(1 + (0.065 × 12)) = 106800
A = $106,800.00
The total amount accrued, principal plus interest, from simple interest on a principal of $60,000.00 at a rate of 6.5% per year for 12 years is $106,800.00.
The simple interest rate for this loan is 78%.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
If Steven borrows $60,000 at an interest rate of 6.5%, the total amount of interest he will pay over 12 years can be calculated as:
I = Prt
where I is the interest, P is the principal amount borrowed ($60,000), r is the interest rate as a decimal (0.065), and t is the time period in years (12). Substituting the given values, we get:
I = 60000 x 0.065 x 12
I = $46,800
The simple interest rate is the ratio of the total interest paid to the principal borrowed, expressed as a percentage:
simple interest rate = (total interest/principal borrowed) x 100
Substituting the given values, we get:
simple interest rate = (46800 / 60000) * 100
simple interest rate = 78%
Therefore,
The simple interest rate for this loan is 78%.
Learn more about simple interests here:
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#SPJ3
n a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $32 and standard deviation of $15. Construct a confidence interval at a 90% confidence level. Enter your answer as an interval (i.e., parentheses) accurate to one decimal place. Confidence interval =
Answer:
($29.698276497364876985)
Step-by-step explanation:
i actually dont know but thnks for the points BTW
What is the value represented by the letter A on the box plot of the data?
10, 12, 15, 21, 24, 30
А
B
с
D
E
Enter your answer in the box.
Which regions have populations with 9 as the power?
Africa and Asia
I did it today in my class
a gardener is planting two types of trees type A is 5 feet tall and grows at a rate of 5 inches per year. Type B is 4 feet tall and grows at a rate of 8 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height
Answer:
the answer is 4 years
Step-by-step explanation:
A square playground has an area of 10,000ft^2. What is the length of one of the slides of the playground?
Answer:
100 feet in length
Step-by-step explanation:
Given the following question:
[tex]A=s^2[/tex]
In order to find the area of the square we have to multiply two of the lengths by itself.
[tex]A=s^2[/tex]
[tex]A=100^2[/tex]
[tex]A=100\times100[/tex]
[tex]100\times100=10000[/tex]
[tex]=10000ft^2[/tex]
Which means one side of the given square is "100 feet."
Hope this helps.
A'B'C' is the image of AABC under a rotation about the origin, ( 0,0).
Determine the angles of rotation.
Choose all answers that apply.
Answer:
90° CCW
Step-by-step explanation:
The angle from C to the origin to C' is a right angle when measured counterclockwise (in the usual direction).
ΔA'B'C' is a rotation of ΔABC 90° CCW.
__
This is fully equivalent to a rotation of 270° CW.
he area of a rectangular piece of metal is 20 square centimeters. The perimeter is 18 centimeters. What are the dimensions of the piece?
Answer:
5 cm by 4 cm
Step-by-step explanation
A = L x W 20 = L x W
P = 2L + 2W (18 = 2L + 2W)/2
9 = L + W W = 9 - L
20 = L (9 - L) 20 = 9L - L^2
L^2 - 9L + 20 = 0 (L - 4)(L - 5) = 0
L = 4 L = 5
The longer one is the length, so L = 5, and W = 4.
What is the discount of a guitar with an original price of $95 and a discount of 15%.
Answer:
$80.75 dollars
Step-by-step explanation:
Given the following question:
Initial price = $95
15% discount
In order to find the answer, we have to find 15% of 95.
[tex]\frac{15\times95}{100} =15\times95=1425\div100=14.25[/tex]
[tex]95-14.25=80.75[/tex]
[tex]g=80.75[/tex]
The guitar (after a 15% discount) costs "$80.75 dollars."
Hope this helps.
Solve for x.
7.82x+1.83<15.42
Enter your answer in the boxes to correctly state the solution. Round your final answer to the nearest hundredth.
x
Answer:
26.44%
Step-by-step explanation:
The change in temperature is:
1535 - 1214 = 321
This change represents a percent increase:
321/1214*100% = 26.44% (rounded)
correctly simplify the expression 1/2 2 x 1/2 x 12 3
Answer:
18
Step-by-step explanation:
1/2 x 12 x 3
1 x 12 x 3/2 -divide all by 2
12 x 3/2 - simplify
36/2
answer: 18
Help????????????????
Answer:
Question 3 - true
Step-by-step explanation:
It is onto function.
Please answer 25 and 26
8 centimeters= ____ millimeters?
Answer: 80
Step-by-step explanation:
1 cm is 10 millimeters. 8*10 is 80
8.0 times 10 negative 5 in standard form
Answer:
75
Step-by-step explanation:
hope this helps
Ben stayed in three different cities (Washington, D.C., Atlanta, Georgia, and Dallas, Texas) for a total of 14 nights. He spent three
times as many nights in Dallas as he did in Washington. The total cost for 14 nights (excluding tax) was $2230. Determine the
number of nights that he spent in each city.
City Cost per Night
Washington $200
$140
Dallas
$150
Atlanta
Answer:
Step-by-step explanation:
w + a + d = 14
d = 3w
200w + 150a + 140d = 2230
w + a + 3w = 14
4w + a = 14 Eq. 1
200w + 150a + 140d = 2230
20w + 15a + 14(3w) = 223
62w + 15a = 223 Eq. 2
Eq. 1 & Eq. 2
4w + a = 14
62w + 15a = 223
-60w - 15a = -210
62w + 15a = 223
2w = 12
w = 6.5
A half a night is not allowed. Are you sure of rates in each city?
Is it Washington $200,
Dallas $140
Atlanta $150
It doesn't work.
I need help please 36 points
Using the power of zero property, we find that:
a) The simplification of the given expression is 1.
b) Since , equivalent expressions are: and .
--------------------------------
The power of zero property states that any number that is not zero elevated to zero is 1, that is:
Thus, at item a, , thus the simplification is .
At item b, equivalent expressions are found elevating non-zero numbers to 0, thus and .
PLEASE HELP ME. I DESPERATELY NEED IT
Write the point slope form of the equation of the line through the given point and slope:
EXPLAIN PLEASE. STEP BY STEP
hmm wait for my answer
Step-by-step explanation:
wait
Answer: [tex]y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]
=====================================================
Explanation:
The given slope is [tex]m = \frac{4}{3}[/tex] and the line goes through the point [tex](x_1,y_1) = (3,-1)[/tex]
This means [tex]x_1 = 3 \ \text{ and } \ y_1 = -1[/tex]
We will plug this information into the point-slope formula below and simplify.
[tex]y - y_1 = m\left(x - x_1\right)\\\\y - (-1) = \frac{4}{3}\left(x - 3\right)\\\\y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]
We stop here since your teacher wants the answer in point-slope form. As the name implies, point-slope form is very handy to quickly spot the slope and a point on the line.
If your teacher wanted the answer in slope-intercept form, then you'd solve for y to get it into y = mx+b form.
What is the 2nd term of the linear sequence below? − 5 , − 7 , − 9 , − 11 , − 13
Answer:
-15
Step-by-step explanation:
it is subtracting by 2
Alan saves $180 each month. How much has Alan saved after 3 years?
$540
O $1,620
O $3,240
O $6,480
Answer:
$6,480
Step-by-step explanation:
[tex]180(12)(3)=6,480[/tex]
Hope this helps
Answer:
#540
Step-by-step explanation:
Alan saved $180 in each month
and we have 12 months in a year so we say
$180=12
x=36
here we cross multiply then we have 180 * 36 which is equal to $6480 after that we divide it by 12 and that's $540
Note: I got 36 months because 12 months in a year so multiply by three years that's 36 months
Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay. A. 4. 9 b. 8. 5 c. 14. 6 d. 17. 1.
The total employee benefits of Trevor with no job expenses and gross pay of $28600 is 17.1%. Option d is the correct option.
What is total employment compensation?Total employment compensation is equal to the sum of gross pay and employment benefit subtracted with any job expenses.
Trevor’s total employment compensation is $33,500. Trevor has no job expenses and his gross pay is $28,600.
Let the total employee benefits is x. Therefore, using the above definition of total employment compensation,
[tex]33500=28600+x-0\\[/tex]
Solve it for x as,
[tex]x=33500-28600\\x=4900[/tex]
In the percentage form,
[tex]x=\dfrac{4900}{28600}\times100\\x=17.1\%[/tex]
Hence, the total employee benefits of Trevor with no job expenses and gross pay of $28600 is 17.1%. Option d is the correct option.
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Write an equation the describes the line passing through point (1/2, 0) with slope - 1
Answer:
Your equation is [tex]y = -1x + \frac{1}{2}[/tex] or [tex]y = -1x + .5[/tex]
Step-by-step explanation:
Equation of the line: [tex]y=mx+b[/tex]
Add in the slope in place of ([tex]m[/tex])
[tex]y=-1x+b[/tex]
Add in the x value of the given point in place of ([tex]x[/tex])
[tex]y=(-1)\frac{1}{2}+b[/tex]
Add in the y value of the given point in place of ([tex]y[/tex])
[tex]0=(-1)\frac{1}{2} + b[/tex]
—
Solve:
[tex]0=(-1)\frac{1}{2} +b[/tex]
Multiply -1 and [tex]\frac{1}{2}[/tex]
[tex]-1 *\frac{1}{2}=-\frac{1}{2}[/tex]
So,
[tex]0=-\frac{1}{2} +b[/tex]
Now, add [tex]-\frac{1}{2}[/tex] to 0
[tex]0=-\frac{1}{2} +b[/tex]
[tex]+\frac{1}{2}[/tex] [tex]+\frac{1}{2}[/tex]
---------------------------
[tex]\frac{1}{2} = b[/tex]
Replace ([tex]b[/tex]) with [tex]\frac{1}{2}[/tex]
Your equation is [tex]y = -1x + \frac{1}{2}[/tex] or [tex]y = -1x + .5[/tex]
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
A watch, after allowing a discount of 15% on its marked price, was sold at a gain of 20%. Had it been sold after allowing 25% discount there would have been gain of Rs. 120. Find the cost price of the watch.
Answer:
Answer:1200
Step-by-step explanation:
Consider the cost price to be x.
1st equation x - (15/100)x = x + (20/100) ...15% discount and gain of 20%
2nd equationx - (25/100)x = x + 120 ....25% discount and a gain of 120Rs
Solving above equations by subtracting we get
(10/100)x = (20/100)x - 120
Solving LHS and RHS..(10/100)x =120
x=1200
Convert mixed number 1 1/4 x 2/3
Answer:
5/4 x 2/3
it just means take the 1 and make it 4/4 instead then add the other 1/4