Answer:
6 + 12/13, or 90/13 people will be served
Step-by-step explanation:
Ratios stay the same, no matter the quantity.
Given this, we can say that (13 grapes / 3 people) = (30 grapes / x amount of people)
13/3 = 30 / x
multiply both sides by 3 to remove a denominator
13 = 30 * 3 /x
multiply both sides by x to remove the other denonimator
13 * x = 30 * 3
13 * x = 90
divide both sides by 13 to isolate the x
x = 90/13 = 6 + 12/13 ≈6.92 people
Write the following statement in equation form using variables x and y. "Sum of two numbers is 15 and difference is 11.
Answer:
see explanation
Step-by-step explanation:
Using x and y to represent the 2 numbers with x > y , then
x + y = 15 → (1)
x - y = 11 → (2)
Adding the 2 equations term by term to eliminate y
2x = 26 ( divide both sides by 2 )
x = 13
Substitute x = 13 into (1)
13 + y = 15 ( subtract 13 from both sides )
y = 2
The 2 numbers are 13 and 2
Convert 13pi/6 to a degree measure
A=390
B=2450.44
C=30
D=780
Answer:
390 degrees
Step-by-step explanation:
The conversion factor is 180/pi
13 pi /6 * 180/pi
13/6 *180
390
PLEASE HELP
Find the probability of “landing” in the shaded region of the figures below.
Answer:
Hello,
p=0.1024
Step-by-step explanation:
The probability is the ratio of the areas of the 2 circles:
[tex]p=\dfrac{\pi*8^2}{\pi*25^2} =\dfrac{64}{625} =0.1024[/tex]
Answer:
64/625.
Step-by-step explanation:
Probability = area of small circle / area of the large one
= 8^2 / 25^2
= 64/625
Numeric Response 4. In an arithmetic series, the first term is -12 and the 15th term is 40. The sum of the first 15 terms is (Record your answer in the numerical-response section below.)
Your answer should be in.0000
In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.
If the 15th term is 40, then
40 = -12 + (15 - 1) c ==> c = 52/14 = 26/7
We can then write the n-th term as
-12 + (n - 1) 26/7 = (26n - 110)/7
The sum of the first 15 terms is then
[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]
Another way to compute the sum: let S denote the sum,
S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40
Reverse the order of terms:
S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12
Notice that adding up terms in the same position gives the same result,
-12 + 40 = 28
-58/7 + 254/7 = 28
-32/7 + 228/7 = 28
so that
S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28
There are 15 terms in the sum, so
2S = 15×28 ==> S = 15×28/2 = 210
calculate the area of shaded region
Answer:
528 cm squared
Step-by-step explanation:
A parallelogram (slanted shape at the bottom) is essentially the same area as a rectangle.
Therefore, both shapes have the same measurements.
Multiply the length and height of the rectangle to get its area: 22cm×12cm =264cm squared
Since the area of the rectangle corresponds geometrically to the area of the parallelogram, just multiply the area of the rectangle (264cm squared), by 2.
So 264×2, = 528cm squared
Ta da...
 Which correlation best describes the data below.
no correlation
weak positive
strong positive
strong negative
Answer:
strong positive
Step-by-step explanation:
both variables are moving in the same direction and is nearly a line
As x increases, y increases. This has a strong positive correlation
For a party Justin buys a pizza and cuts it into 24pieces.Marc eats 1/6 of portion of the pizza and claudine eats 1/4 of what remains after both of them have eaten, Sylvia eats 1/3 of the result.Justin gets to eat what is left over what fraction of the pizza did Justin not eat
Answer:
Justin did not eat 7/12 of the pizza
Step-by-step explanation:
Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over
Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over
Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over
Justin eats 10.
24 - 10 = 14
Justin did not eat 14/24 = 7/12
Find an equation of the line having the given slope and containing the given point m= - 8, (2,5) The equation of the line is y= (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression)
Answer:
Equation of line is y = -8x + 21
Step-by-step explanation:
Slope, m = -8
General equation of line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
At point (2, 5), y = 5 and x = 2:
[tex]{ \tt{5 = ( - 8 \times 2) + c}} \\ { \tt{c = 21}}[/tex]
Therefore:
[tex]{ \sf{y = - 8x + 21}}[/tex]
[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]
The points A,B,C and D divide the line segment AD in the ratio 4:3:1 , respectively , and AD = 72cm . What is the length of BD?
Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;
XZ = XY + YZ
The length of the segment BD is 36 cm
The reason the above value is correct is as follows:
Known:
The ratio in which the points A, B, C, and D divide the line segment = 4:3:1
The length of segment AD = 72 cm
Required:
The length of BD
Method:
Calculate the length of BC and CD and add their values to get BD
Solution:
Let the ratios be given unit proportions of the segment AD such that we have;
AB = 4 units
BC = 3 units
CD = 1 unit
By segment addition postulate, we have;
AD = AB + BC + CD
∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm
∴ 1 unit = 72 cm/8 = 9 cm
1 unit = 9 cm
BD = BC + CD by segment addition postulate
BC = 3 units = 3 × 1 unit
∴ BC = 3 × 9 cm = 27 cm
BC = 27 cm
CD = 1 unit
∴ CD = 9 cm
∴ BD = 27 cm + 9 cm = 36 cm
The length of segment BD = 36 cm
Learn more about segment addition postulate here:
https://brainly.com/question/17015321
1. 6/5 x 3/4
2. 2/3 x 8/5
3. 5/2 x 4/3
Answer:
hope this might help you
Solve for the following. Type your answer using digits. A rectangle with a length ofx−4 and a width of 8 has a perimeter of 34. The value of x is .
Answer:
length = 13
Step-by-step explanation:
length =x-4
width = 8
perimeter =2( x-4) + 2× 8 = 34
= 2x - 8 + 8 =34
= 2x =34
= x = 17
Answer:
x = 13
Step-by-step explanation:
The opposite sides of a rectangle are equal, then
2(x - 4) + 2(8) = 34 ← distribute parenthesis and simplify left side
2x - 8 + 16 = 34
2x + 8 = 34 ( subtract 8 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13
The number of pounds of one-dollar-a-pound
coffee needed to mix with 80 pounds of 70¢ a
pound coffee to make a mixture worth 84¢ a
pound is
(A) 70
(B) 80
(C) 95
(D) 65
Answer:
A
Step-by-step explanation:
Let's say we need x pounds of one-dollar-a-pound coffee . The coffee must average out to 84 cents a pound, and the formula for average is
sum of cost of coffee / number of pounds of coffee, so we have
0.84 = total cost of coffee / (x+80) . The total cost of coffee can be found to be the sum of the cost of $1 coffee and 70 cent coffee, so we have
0.84 = (cost of $1 coffee + cost of 70 cent coffee) / (x+80)
The cost of $1 coffee can be found by adding $1 for each pound of one dollar coffee, or $1 * x. Similarly, the cost of 70 cent coffee is equal to 0.70 * 80, so we have
0.84 = (1*x+0.7*80)/(x+80)
0.84 = (x+56)/(x+80)
multiply both sides by (x+80) to remove a denominator
0.84(x+80) = x+56
0.84x + 67.2 = x+56
subtract both sides by 56 and 0.84x to isolate the x and its coefficients
11.2 = 0.16 x
divide both sides by 0.16 to isolate x
11.2/0.16 = x = 70
The number of pounds of a constituent in a mixture given the cost of the
mixture and the cost and mass of the other constituent can be calculated
by using an equation to model the system
The correct option for the number of pounds of one-dollar- pound coffee needed is option A
(A) 70 pounds
The procedure for arriving at the correct option is as follows:
The given parameters are;
The cost of the the coffee for which the mass in the mixture is to be determined = One-Dollar a pound = 100 ¢ a pound
The mass of the coffee 70¢ a pound coffee to be mixed = 80 pounds
The cost per pound of the mixture = 84 ¢ a pound
The required parameter;
The number of pounds of the one-dollar-a-pound (100 ¢ a pound) coffee in the mixture
Method:
Let x (pound) represent the number of pounds of the one-dollar-a-pound coffee in the mixture, we have;
Mass of mixture = Mass of the one-dollar-a-pound in the mixture, x + Mass of 70 ¢ a pound in the mixture, 80
∴ Mass of mixture in pounds = x + 80
Cost = Cost per pound × Number of pound
Find solution by applying the equation;
Cost of the constituents = Cost of the mixture
Where;
Cost of the constituents = $1 × x + 70 ¢ × 80 = 100 ¢ × x + 70 ¢ × 80
Cost of the mixture = 84 ¢ × (x + 80)
Therefore;
100 ¢ × x + 70 ¢ × 80 = 84 ¢ × (x + 80)
The above can be expressed as 100·x + 70×80 = 84 × (x + 80)
Expanding, evaluating and collecting like terms gives;
100·x + 5,600 = 84·x + 6,720
100·x - 84·x = 6,720 - 5,600 = 1,120
16·x = 1,120
x = 1,120/16 = 70
The number of pounds of one-dollar- pound coffee needed, x = 70 pounds
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Klog earns $6.30 per hour. He worked 3.5 hours each day Monday through Friday plus 4 on Saturday. How much did he earn altogether?
Answer:
Klog earned $135.45 altogether.
Step-by-step explanation:
Hours
Monday - Friday : 5 days / 3.5 hours
Saturday : 1 day / 4 hours
3.5 · 5 + 4
= 17.5 + 4
= 21.5
Money
$6.30 per hours / 21.5 hours
6.30 · 21.5
= $135.45
I need help with VOCAB!!!Please help ASAP
Answer:
SSS postulate
Step-by-step explanation:
its probab;py wrong im sorry
Answer:
SSS Postulate
Step-by-step explanation:
Since both triangles have 3 congruent sides, then
The triangles are congruent by the SSS postulate
Help anyone can help me do this question,I will mark brainlest.
Answer:
8 cm
Step-by-step explanation:
AM = MC = BM = (1/2) BC => AM , MC , BM = 5, => BC = 10apply pytago => (AC ^ 2) + (AB ^ 2) = (BC ^2)AB = [tex]\sqrt{BC ^2 - AC ^2}[/tex] = [tex]\sqrt{10 ^2 - 6 ^ 2}[/tex] = 8 (cm)Answer:
4
Step-by-step explanation:
So first let's write the information we got
Angle BAC = 90 degrees
Midpoint of BC = M
AC = 6cm
Am= 5cm
Also I found MC = BM, since it has a line that represents both lines are same
so to find it we have to Pythagoras theorem (A^2 + B^2 = C^2), well it is question we have the 'A value and C Value', also we need to find the value of B to find the length of MC and BM
A = 5
C = 6
so therefore to find B^2, we have to do the reverse, we don't add but subtract
C^2 - A^2 = B^2
___________________________________________________________
Moving on to Calculation
6^2 - 5^2 = B^2
36 - 25 = B^2
B^2 = 9
B = √9
B = 3
MC and BM Length = 3 cm
____________________________
Now, we know the length we again need to use Pythagoras theorem to solve this.
Since we know
A = 5
B = 3
So..
A^2 + B^2 = C^2
5^2 + 3^2 = C^2
25 - 9 = C^2
C^2 = 16
C = √16
C = 4
a grocery store buys boxes of cereal for $ 2.00 each and sells them for 50% more. what does the grocery store charge its customers for each box of cereal?
Answer:
$3.00
Step-by-step explanation:
First find the markup
2.00 * 50%
2 * .5
1
Add this to the original price
2+1 =3
The store sells the cereal for $3.00
Answer:
$3
Step-by-step explanation:
The grocery store pays $2.00 for each box of cereal bought.
First, find 50% of the cost of each box:
2.00 x 0.50 = 1.00
Next, add the additional amount to the starting price:
2.00 + 1.00 = $3.00
$3.00 is your answer.
~
Simplify 2m^2 – 2m + 3m^2
Answer:
5m^2-2m
Step-by-step explanation:
2m^2-2m + 3m^2
5m^2-2m
Answer:
5m² - 2m
Step-by-step explanation:
Given
2m² - 2m + 3m² ← collect like terms
= (2m² + 3m²) - 2m
= 5m² - 2m
10.5125 rounded to the nearest cent plz help me ty <3
Answer: your answer should be 10.5130
Step-by-step explanation:
If (5^(k-1))+(5^(k+1)) = m, what is 2*5^k in terms of m?
If [tex]5^k^-^1+5^k^-^1=m[/tex], what is [tex]2*5^k[/tex] in terms of m?
A) 5m
B) 5m÷2
C) 5m÷13
D) 5m÷26
Answer:
5m
Step-by-step explanation:
5^(k-1)+5^(k-1)=m
Going to combine like terms on left:
2×5^(k-1)=m
Law of exponents applied:
2×5^k×5^(-1)=m
Reciprocal:
2×5^k×1/5=m
Multiply 5 on both sides to obtain the requested:
2×5^k=5m
Write an equation of the line. What is the equation of the line?
Answer:
y=-1
Step-by-step explanation:
As the line is horizontal in nature and pass through (2,-1), the equation is y=-1
a teacher had 23 pupils to her class. all but 7 of them went on an excursion trip and thus were away for the day. how many students remains in the class that day.
Answer:
16
Step-by-step explanation:
If the teacher had 23 but then 7 had to go away for a trip, then all you do is subtract 23 and 7:
23-7= 16
Thus, the teacher had 16 students that day after the 7 went away.
The blue team scored two more than five times the number of points,p, scored by the red team
Write an expression for the problem
Answer:
2 + 5p
Step-by-step explanation:
Hi there!
Let [tex]p[/tex] equal the number of points scored by the red team.
We're given:
The blue team scored two more than five times the number of points scored by the red team.
⇒ blue team points = 2 + (5 × red team points)
⇒ blue team points = 2 + 5p
I hope this helps!
find the missing length for the following trapezoid
Answer:
15 is the answer I think.
A polynomial has one root that equals 2 + i. Name one other root of this
polynomial.
Answer:
sorry
Step-by-step explanation:
polynomial is not given
question is incomplete
A number is doubled and 7 is subtracted from the answer, if the result is -25.
-create an equation
-solve the equation to find the number
Please Respond
$108.75 for working 15 hours as a holiday helper wrapping gifts. At this rate, how much money will she earn if she works 18 hours the next week. Explain.
Choose which is a statistical question: What are
the ages of the students in this class? or How
many pennies equal 1 dollar? Explain.
The statistical question is; "What are the ages of the students in this class?
What is a statistical question?A statistical question is always aimed at data collection which can subsequently used for analysis and decision making. Statistical questions are asked in the course of research.
Among the two questions, the statistical question is; "What are the ages of the students in this class?
Learn more about statistics:https://brainly.com/question/8058700
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If Malcolm selects two coins at random without replacement, what is the probability (as decimal) that he selects a nickel followed by a dime? Penny 8 Nickel 6 Dime 8 Quarter 7
Answer:
65
Step-by-step explanation:
because
Answer:
1st coin: the probability for it to be a nickel is 6/29.
the 2nd coin, the probability for it to be a dime is 8/28.
total probability is 6/29 * 8/28 = 14/203.
can someone please help me solve this?
Answer:
-15
Step-by-step explanation:
df(x, y) / dy = lim (f(x, y+h) - f(x, y)) / h =
lim (e^x^2 - 15y - 15h - e^x^2 ‐ 15y) / h = lim -15h / h = -15
so, the first derivative of f(x,y) by y is simply a constant : -15
fy (x, y) = -15 for any and every values of x and y.
the fast track would be derivative calculation :
the derivative by y makes x a constant. and every constant is eliminated for derivation.
so, e^x^2 goes away (= 0 in the derivative).
that leaves -15y = -15×y¹. its derivative simply is
1×-15×y⁰ = -15
A recipe for eight flapjacks needs 2oz of butter, 3oz of sugar, and 4 oz of rolled oats. How many flapjacks can I make if I have 14 oz of butter, 15 oz of sugar, and 16 oz of rolled oats?
Answer:
Step-by-step explanation:
Eight flapjacks
2oz of butter
3oz of sugar
4 oz of rolled oats.
Each flapjack
Butter = 2/8 = 1/4 oz
Sugar = 3/8 oz
Rolled oats = 4/8 = 1/2 oz
How many flapjacks can I make if I have
14 oz of butter,
15 oz of sugar, and
16 oz of rolled oats?
Butter
= 14 oz ÷ 1/8 oz
= 14 × 8/1
= 112 flapjack
Sugar
= 15 oz ÷ 3/8 oz
= 15 × 8/3
= 120/3
= 40 flapjacks
Rolled oats
16 oz ÷ 1/2 oz
= 16 × 2/1
= 32 flapjack
Therefore,
Considering the quantity of rolled oats available, the number of flapjacks that could be made is 32
