ANSWER
The solution is (2,1)
EXPLANATION
The given equations are:
2x+4y=8...(1)
3x-5y=1...(2)
We make x the subject in the first equation to get:
2x=8-4y
This means that,
x=4-2y...(3)
Put equation (3) into equation (2)
3(4-2y)-5y=1
Expand:
12-6y-5y=1
-6y-5y=1-12
-11y=-11
y=1
Put y=1 into equation (3).
x=4-2(1)=2
The solution is (2,1)
Marlena must answer three out of eight essay questions on her writing test. How many ways can she choose 3
Answer:
Your answer should be 56
Marlena can choose 3 out of 8 essay questions in 56 different ways.
The question asked by the student is related to combinations in mathematics. Marlena must choose 3 out of 8 essay questions on her writing test. To determine how many ways Marlena can choose 3 questions, we use the formula for combinations:
C(n, k) = n! / [k! * (n - k)!]
Where n is the total number of items to choose from (in this case, 8 questions), and k is the number of items to choose (3 questions). The symbol '!' represents a factorial, which is the product of all positive integers up to that number. So we calculate as follows:
Calculate the factorial of n (8! = 8*7*6*5*4*3*2*1).Calculate the factorial of k (3! = 3*2*1).Calculate the factorial of n - k (8-3)! = 5! = 5*4*3*2*1).Put it all together in the formula to find the number of combinations: C(8, 3) = 8! / [3! * (8 - 3)!]This simplifies to:
C(8, 3) = (8*7*6) / (3*2*1) = 56
Therefore, Marlena has 56 different ways to choose 3 out of the 8 essay questions.
Maddie wants to build a circular fence around her yard. The yard has a radius of 7 feet, what is the circumference? Use 3.14 for π.
A) 43.96
B) 53.86
C) 99.02
D) 100.12
Answer:
43.96 ft, or about 44 ft
Step-by-step explanation:
C = 2πr. Here, π is approx. 3.14 and r is 7 ft. Thus, the circumference of the yard is
C = 2(3.14)(7 ft) = 43.96 ft
Answer:
it is A
Step-by-step explanation:
Determine the measure of ∠FGC. A) 22° B) 70° C) 110° D) 120°
Answer:
C
Step-by-step explanation:
Answer: C) 110
Step-by-step explanation:
After jogging 3 miles bobby checked his heart rate he counted 30 beats and 15 seconds what would his heart rate be for one minute
Answer:
Step-by-step explanation:
First, i would add 15 until you get to 60, or divide.
15 / 60 = 4
Then multiply 30 by 4: 30 X 4 =120.
120 is the awnser.
If the coefficient of determination for a data set is 0.25 and the SEA for the data set is 12, what is the SST for the data set
A. 16
B. 20
C. 8
D. 12
Answer:
A
Step-by-step explanation:
We can use a simple formula to solve for SST. The formula is:
[tex]SST=\frac{SSE}{1-R^2}[/tex]
Where
the coefficient of determination is [tex]R^2[/tex]
Now, we are given [tex]R^2[/tex] is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:
[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]
correct answer choice is A
The location of point V is (-3,3). The location of point X is (9,13). Determine the location of point W which is 3/4 of the way from V to X
ANSWER
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
EXPLANATION
We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.
The x-coordinate of this point is given by:
[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]
[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]
[tex]x= \frac{21 - 12}{4 + 3} [/tex]
[tex]x= \frac{9}{7} [/tex]
The y-coordinates is given by;
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]
[tex]y= \frac{39+12}{4 + 3}[/tex]
[tex]y= \frac{51}{7}[/tex]
Hence
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
John starting playing video games as soon as he got home from school. He played video games for 15 minutes. Then, it took John 45 minutes to finish his homework. When John finished his homework, it was 3:15 P.M. What time did John get home from school?
Answer:
2:15
Step-by-step explanation: First you - 15 by 3:15 which = 3:00 then - 45 by 3:00 or 60 - 45 = 15. so therefore 2:15 is the answer. Have a good day, hope I helped
I REALLY NEED HELP!! WILL MARK BRAINLIEST!
Which question is best modeled with a division expression?
A. How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?
B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?
C. How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?
D. How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?
Choice D, because you would have to divide 3 1/2 by 2 to find the answer
the rest are either subtraction or multiplication
Answer:
Option D is best modeled with a division expression
Step-by-step explanation:
A) How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?
Cost of 1 pound = $2
Cost of 3 and 1/2 pounds = [tex]2 \times 3.5[/tex]
B) B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?
1 pie requires 3.5 apples
So, 2 pies requires apples = [tex]3.5 \times 2[/tex]
C) How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?
Recipe requires 3.5 apples
You have 2 apples
More apples required = 3.5 - 2
D) . How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?
Apples required in 2 pies = 3.5
Apples required in 1 pie = [tex]\frac{3.5}{2}[/tex]
Hence Option D is best modeled with a division expression
Please please help me
Answer:
[tex]\large\boxed{(x-5)^2+(y+7)^2=36}[/tex]
Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We hace the center at (5, -7) → h = 5 and k = -7.
The radius is equal to the distance petween the center and other point on the circumference of a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates of the points (5, -7) and (5, -1):
[tex]d=\sqrt{(5-5)^2+(-1-(-7))^2}=\sqrt{0^2+6^2}=\sqrt{36}=6[/tex]
Therefore the equation of a circle is:
[tex](x-5)^2+(y-(-7))^2=6^2\\\\(x-5)^2+(y+7)^2=36[/tex]
125 freshman, 85 passed the english test, 95 passed statistics test, 15 failed both what is the probability that they passed both
Answer:
0.56
Step-by-step explanation:
125 in total.
Let x be the number of those who passed both tests.
85 passed English, then 85-x passed only English;95 passed statistics, then 95-x passed only statistics;15 failed both.Thus,
x+(85-x)+(95-x)+15=125,
195-x=125,
x=70.
Thus, the probability that they passed both tests is
[tex]Pr=\dfrac{70}{125}=\dfrac{14}{25}=0.56.[/tex]
Which expressions are equivalent to the one below? Check all that apply
64^x
A. 8^2*8^x
B. (8*8)^x
C. 8*8^2x
D. 8*8^x
E. 8^2x
F. 8^x*8^x
Answer:
B, E, F
Step-by-step explanation:
Equivalent expressions are expressions which are equal. To show expressions are equal, reduce to lowest terms by simplifying using exponent rules.
A. 8^2*8^x = 8^2+x
B. (8*8)^x = 64^x
C. 8*8^2x = 8^(2x +1)
D. 8*8^x = 8 ^ (x+1)
E. 8^2x = 64^x
F. 8^x*8^x = 8^(x+x) = 8^(2x) = 64^x
Answer:
8^2x 8^x (8•8)^x
Step-by-step explanation:
A new car is purchased for 19900 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 8 years?
Answer:
[tex]\$10,665.64[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$19,900\\r=7.5\%=0.075\\x=8\ years[/tex]
substitute the values in the formula
[tex]V=\$19,900(1-0.075)^{8}=\$10,665.64[/tex]
Answer: The answer is 10665.64
Step-by-step explanation:
Exponential Functions:
y=ab^x
A= starting value = 19900
r=rate = 7.5%=0.075
Exponential Decay:
b=1-r=1-0.075=0.925
Write Exponential Function:
y=19900(0.925)^x
Plug in time for x:
y=19900(0.925)^8
y= 10665.6404317
Evaluate
y≈10665.64
After the program was completed, the coach monitored each of the 30 athletes for five athletic events. At the end of this process, he reported that the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program. What can be concluded from the coach's report?
Answer:
B
Step-by-step explanation:
How many females with college degrees work at his two stores?
Answer:
30
Step-by-step explanation:
At the northside store there are 12 females with college degrees
At the southside store there are 18 females with college degrees
The total number of females at the two stores with college degrees is
12+18 = 30
There are 10 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible
Final answer:
The number of different subcommittees possible from a board of 10 members when forming a subcommittee of 3 members is 120, calculated using the combination formula C(10, 3).
Explanation:
To calculate the number of different subcommittees possible from a board of directors consisting of 10 members when forming a subcommittee of 3 members, we must use the concept of combinations because the order of selection does not matter. This is a problem of counting without regard to the order and is solved by using the combination formula:
C(n, k) = n! / (k! * (n-k)!) where 'n' is the total number of items to choose from, 'k' is the number of items to choose, 'n!' represents the factorial of n, and 'k!' is the factorial of k.
Here, 'n' is 10 (the total number of board members) and 'k' is 3 (the number of members to be chosen for the subcommittee). Thus, the formula for our calculation is:
C(10, 3) = 10! / (3! * (10-3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Therefore, there are 120 different subcommittees possible when selecting 3 members from a board of 10.
Final answer:
To find the number of different subcommittees possible from 10 members when selecting 3, the combination formula C(n, k) = n! / (k! * (n - k)!)is used, which results in 120 different subcommittees.
Explanation:
The student's question pertains to combinatorics, which is a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Specifically, the student is asking about the number of ways to form a subcommittee of 3 members from a larger committee of 10 members. To solve this, one would use the combination formula, which is used for selecting items from a group without regard to the order in which they are selected.
The combination formula is given by:
C(n, k) = n! / (k! * (n - k)!)
Where:
n is the total number of items to choose from (in this case, 10 board members),
k is the number of items to choose (in this case, a subcommittee of 3 members),
n! (n factorial) is the product of all positive integers up to n,
k! (k factorial) is the product of all positive integers up to k,
(n - k)! is the factorial of the difference between n and k.
Applying the formula to the student's scenario:
C(10, 3) = 10! / (3! * (10 - 3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
So, there are 120 different subcommittees possible when choosing 3 members from a board of 10 members.
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math, which of the following properties will you use?
associative
commutative
distributive
14.(22) = 14.(20 + 2)
We still have 14 multiplying 22 but now it will multiply it by 20 and sum it after multiply by 2
So we have the distributive proppertie.
Answer:
distributive property.
Step-by-step explanation:
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math
22 is written as 20+2
so we got 14(20+2)
to multiply this we distribute 14 inside the parenthesis
we multiply 14 with 20 and then multiply 14 with 2
we are distributing 14 inside the parenthesis so its distributive property.
What are the ratios for sin A and cos A? The triangle is not drawn to scale.
Answer:
The answer is B
Step-by-step explanation:
According to the diagram, which of the following statements about area and perimeter of pentagon ABCDE is true?
A) Area = 25 Perimeter = 20
B) Area = 30 Perimeter = 22.31
C) Area = 33 Perimeter = 12.5
D) Area = 35 Perimeter = 18
Answer:
Option B. Area = 30 Perimeter = 22.31
Step-by-step explanation:
step 1
Find the measure of the sides of the pentagon
Observing the graph
AE= 5 units
ED ----> Applying Pythagoras theorem
ED²=2²+3²=13
ED=√13 units
DC=3 units
BC=4 units
AB ---->Applying Pythagoras theorem
AB²=3²+6²=13
AB=√45 units
step 2
Find the perimeter
P=AE+ED+DC+BC+AB
substitute
P=5+√13 +3+4+√45=22.31 units
step 3
Find the area
The area of the figure is equal to the area of two trapezoids
so
A=(1/2)(2+5)(6)+(1/2)(6+3)(2)=21+9=30 units²
Please answer I’ll rate brainlyest
Answer:
41.8%
Step-by-step explanation:
From the table, the total number of female patients is given as 335. On the other hand, the total number of female patients with type-O blood is given as 140. The probability that a randomly selected female patient will have type-O blood can be calculated as;
the total number of female patients with type-O blood/the total number of female patients
140/335 = 0.4179
As a percentage this becomes;
0.4179 * 100 = 41.8%
Therefore, the percentage of female patients with type-O blood is 41.8%
Find h(-3) if h(x) = x^2 - 2x - 5
Final answer:
To calculate h(-3) for the function h(x) = x² - 2x - 5, we plug in -3 for x and simplify to get a result of 10.
Explanation:
To find h(-3) when given h(x) = x² - 2x - 5, we need to substitute x with -3 into the function and simplify:
h(-3) = (-3)² - 2(-3) - 5
= 9 + 6 - 5
= 15 - 5
= 10.
Therefore, h(-3) equals 10.
Erica went shopping for art supplies. The watercolor set was 30% off its regular price of $20.00. What did she pay for the watercolors?
Answer:
$14.00
Step-by-step explanation:
30% less than 100% of the regular price is 70% of the regular price.
Erica paid ...
0.70 · $20.00 = $14.00
Can someone please explain it please: The jones family paid £1890 for their holiday with shark tours after a 12.5% surcharge was added at the last minute. What did they originally think they would be paying?
By dividing the total amount of £1890 by 1.125, we find that the original price the Jones family thought they would be paying for their holiday was £1680, before the 12.5% surcharge was added.
The Jones family encountered a last-minute surcharge on their holiday package with Shark Tours, which affected the total cost they paid. Given a 12.5% surcharge applied to their original cost, we can calculate the initial price by considering the final amount (£1890) to be 112.5% (100% + 12.5%) of the original price. To find the original price, we divide the total amount by 112.5% (or 1.125 as a decimal).
Original price = Total amount paid / Surcharge rate
We then have:
Original price = £1890 / 1.125
Original price = £1680
Therefore, the Jones family originally thought they would be paying £1680 for their holiday before the surcharge was added.
Chantelle had signed up for hockey. Her parents set a limit of $400 for costs for the season. It costs $250 to sign up plus $5 for each ice-time. What is the maximum number of ice-times that Chantelle can go to.
Answer:
30 times
Step-by-step explanation:
subtract 250 from 400, then divide the number (150) by 5 to get your answer 30.
What is the center of the circle given by the equation below?
A. (-4 , -8)
B. (4 , -8)
C. (4 , 8)
D. (-4 , 8)
Answer:
C: (4, 8)
Step-by-step explanation:
Rewrite the given equation x² - 8x = -y² + 16y - 44 in std. form:
x² - 8x + 16 - 16 + y² - 16y + 64 = 64 - 44, or
(x - 4)² + (y - 8)² = 64 - 44 + 16
Comparing this to (x - h)² + (y - k)² = 6²
we see that h = 4 and k = 8. The radius is 6. The center is at (4, 8) (Answer C).
Find the area of the following circle. (Round answer to the nearest hundredth.) d = 15 in area = square inches circumference = inches
The area of a circle with a diameter of 15 inches is 176.63 square inches and the circumference is 47.1 inches, using the formulas A = (pi)r² and C = (pi)d with (pi) approximated as 3.14.
The area and circumference of a circle can be calculated using the formulas A = (pi) r² for the area, and C = (pi) d for the circumference, where r is the radius, d is the diameter, and (pi) is approximately 3.14.
Given the diameter d = 15 inches, we first find the radius by dividing the diameter by 2, which gives us r = 7.5 inches. We then use the area formula to calculate:
Area = (pi) r² = 3.14 ×(7.5 inches)²
Area = 3.14 ×56.25 square inches
Area = 176.625 square inches
After rounding to the nearest hundredth, we get:
Area = 176.63 square inches
For the circumference, we use the formula:
Circumference = (pi) d = 3.14 ×15 inches
Circumference = 47.1 inches
A rectangle has vertices at the points A(-7,-5), B(-2,-5), C(-2,-1), and D(-7,-1). What is the area of the rectangle?
Answer:
20
Step-by-step explanation:
area of a rectangle is determined by length times width so 5 units lies between -7 and -2; and 4 units lie between -5 and -1
The area of the rectangle with given vertices is calculated as the product of the lengths of two adjacent sides, resulting in 20 square units.
To find the area of the rectangle with vertices at A(-7,-5), B(-2,-5), C(-2,-1), and D(-7,-1), you can calculate the lengths of adjacent sides and multiply them together. The length of side AB is the difference in the x-coordinates of A and B, which is |-2 - (-7)| = 5. Similarly, the length of side AD is the difference in the y-coordinates of A and D, which is |-1 - (-5)| = 4.
Therefore, the area of the rectangle is 5 units times 4 units, which equals 20 square units.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
Answer: b) rolled three times, number of 2s rolled
d) rolled twice, number of odds rolled
Step-by-step explanation:
A binomial experiment must meet the following criteria:
There must be a fixed number of trials (rolls) Each trial (roll) is independent of the others There are only two outcomes (success or fail) The probability of each outcome remains constant from trial to triala) rolled twice --> satisfies #1 & #2 (n = 2)
X is the sum --> fails #3 (more than two outcomes)
b) rolled three times --> satisfies #1 & #2 (n = 3)
X is the number of 2s rolled --> satisfies #3 & #4 (P success = 1/6)
c) rolled an unknown number of times - fails #1
d) rolled twice --> satisfies #1 & #2 (n = 2)
X is the number of odds rolled --> satisfies #3 & #4 (P success = 1/2)
Please help me with this
Answer:
294.5 m²
Step-by-step explanation:
shaded region = area of major sector + area of triangle
central angle of major sector = 360° - 130° = 230°
area of sector = area of circle × fraction of circle
A = π × 11.1² × [tex]\frac{230}{360}[/tex]
= [tex]\frac{x11.1^2(230)\pi }{360}[/tex] ≈ 247.3 m²
area of triangle = 0.5 × 11.1 × 11.1 × sin130° ≈ 47.2 m²
shaded area = 247.3 + 47.2 ≈ 294.5 m²
Answer:
294.5 m^2 to the nearest tenth.
Step-by-step explanation:
First work out the area of the blue sector (not including the triangle):
The measure of the large arc = 360 - 130 = 230 degrees and the area of the Whole circle is π(11.1)^2 so, by proportion:
Area of the large sector = 230/360 * π(11.1)^2
= 247.30 m^2.
The area of the triangle = 1/2 * 11.1^2 sin 130 = 47.19 m^2.
So the area of the whole shaded region is 247.30 + 47.19
= 294.49 m^2 (answer)
N a flower garden, there are 4 tulips for every 8 daisies. If there are 32 tulips, how many daisies are there?
Answer: 64 daisies
Step-by-step explanation:
8 x 4 = 32 8 x 8 = 64 daisies
Find the measure of x for this shape.
A. 36
b.28
c.32
d.22
let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.
The same is true for the isosceles triangle on the right side. Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.
Check the picture below.