We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
what is common factors ?The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM). A number that divides two or more numbers precisely is referred to as a common factor. For instance, because they are both even, 10 and 20 share a common factor of 2. The largest number that precisely divides two or more numbers is known as the greatest common factor (GCF).
given
32 girls and 24 boys
Additionally, we must divide them into groups in order to determine the number of groups that can be formed. To do this, we must determine the highest common factor between 24 and 32.
To obtain that, we can express both of these as a prime number product as follows:
24 = 2*2*2*3
32 = 2*2*2*2*2
The highest common factor between 24 and 32 is 2*2*2 = 8 since in all of these we have three times the factor 2.
Each squad will have the following number of boys 24/8 = 3
Each team will have four girls, or 32/8, total.
We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
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Tina puts the letters of the word RADAR on pieces of paper and puts the pieces in a bag. She
draws two letters without looking. The first piece of paper is not replaced before the second
piece is drawn. What is the probability that Tina draws an R twice?
Answer:
1/10
Step-by-step explanation:
the probability of drawing r the first time is 2/5, if tina had gotten the r the first time, the probability of drawing r on the second time is 1/4, so the probability tina draws an r twice is 2/5 * 1/4, or 2/20, or 1/10
how can I solve for x? Answers ASAP
Using the inscribed angle theorem, the value of x is: 9.
What is the Inscribed Angle Theorem?Note that an intercepted arc is regarded as part of the circumference of a circle, which is between a chord and a tangent. Thus, based on the inscribed angle theorem, the inscribed angle measure = 1/2(the intercepted arc measure).
So, we would have:
m∠DEF = 1/2(arc DE)
m∠DEF = 4x + 19
arc DE = 360 - (28x - 2) = 360 - 28x + 2
arc DE = 362 - 28x
Plug in the values
4x + 19 = 1/2(362 - 28x)
Solve for x
2(4x + 19) = 362 - 28x
8x + 38 = 362 - 28x
8x + 28x = 362 - 38
36x = 324
x = 324/36
x = 9
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I just need help on what the answer is and understanding this question, thank you.
The graph represents the potential area of a concrete rectangle, based on length and width.
Which inequality in vertex form represents the graphed region?
A)y less-than negative 2 (x + 16) squared minus 32
B)y less-than negative one-half (x minus 16) squared + 32
C)y less-than negative 2 (x minus 16) squared + 32
D)y less-than negative one-half (x + 16) squared minus 32
The inequality of the graph is y < -1/2(x - 16)^2 + 32
How to determine the inequality?A quadratic function is represented as:
y = a(x - h)^2 + k
The vertex of the graph is
(h, k) = (16, 32)
So, we have:
y = a(x - 16)^2 + 32
The graph pass through the point
(x, y) = (12, 24)
So, we have:
24 = a(12 - 16)^2 + 32
Evaluate the like terms
-8 = a(-4)^2
This gives
16a = -8
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x - 16)^2 + 32
y = -1/2(x - 16)^2 + 32
The graph is a less than graph.
So, we have
y < -1/2(x - 16)^2 + 32
Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32
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Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes.Solve the inequality. How many pounds of tomatoes can Lisa buy
Answer:
At maximum, she can buy 5 tomatoes.
Step-by-step explanation:
If you solve the inequality, as so:
1.2x+1.8 <=7.8
1.2x <= 6
x <= 5
An Annuity Immediate Has 32 Initial Quarterly Payments Of 20 Followed By A Perpetuity Of Quarterly Payments Of 25 Starting In The 9th Year. Find The Present Value At A Nominal Rate Of 16%
The present value of the nominal rate of the annuity will be $535.
How to calculate the annuity?Annuity amount = 20
Number of annuities = 32
APR = 16%
PV of annuities = 357
Number of years to perpetuity = 8
Quarterly perpetuity = 25
PV of perpetuity at 9th year = 625
PV of perpetuity today = 178
Total PV = 357 + 178 = 535
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which of the following is an exponential function y=x^1/2 y=2x^3 y=3^x
Answer:
(c) y = 3^x
Step-by-step explanation:
A function is described as exponential if the independent variable is found in the exponent.
Choicesy = x^(1/2) . . . a square root function, not exponential
y = 2x^3 . . . . a cubic (polynomial) function, not exponential
y = 3^x . . . . . an exponential function
The sides of a rectangle are enlarged by a scale factor of 2. Write
down the scale factor that the area is enlarged by.
Answer:
4
Step-by-step explanation:
both sides are multiplied by 2 which means its the original area*2*2 which means it's the original area*4
Two cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the end of 2 hours, the two cars are 220 miles apart. Find the average speed in mph of the other car.
The speed of an object is the relationship between the distance covered by the object and the time taken. Thus, the average speed of the other car is 30 mph.
The speed of an object is the relationship between the distance covered by the object and the time taken. The expression for speed is given as;
speed = [tex]\frac{distance covered}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the distance of the first car after 2 hours can be determined as:
distance = 80 mph x 2 h
= 160 miles
The distance covered by the first car after 2 hours is 160 miles.
Thus, since the total distance between the two cars after 2 hours is 220 miles, then;
distance covered by the second car = 220 miles - 160 miles
= 60 miles
The distance covered by the second car is 60 miles.
So that the average speed of the other car is;
speed = [tex]\frac{60}{2}[/tex]
= 30 mph
The average speed is 30 miles per hour (mph).
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solve asap please!!!
Graph line y=-1/4x+3
Answer:
connect the points (0, 3) and (4, 2)
To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
The divisor of the expression 2/3 ÷ 6/5 is 9.
We have,
Expression:
2/3 ÷ 6/5
The concept used.
a/b ÷ c/d = ad / bc
Now,
2/3 ÷ 6/5
This can be written as,
= 2/3 x 5/6
= (2 x 5) / (3 x 6)
= 10 / 18
= 2 x 5 / 2 x 9
Cancel the common factor.
= 5 / 9
This can be read as,
Dividend = 5
Divisor = 9
Thus,
The divisor of the expression is 9.
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Question
The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Find the location of the earthquake's epicenter if it is 2 miles away from A(−2,5), 4 miles away from B(2,3), and 7 miles away from C(−2,−4).
Answer:
The epicenter is ( - 2, 3)Step-by-step explanation:
Let the epicenter be E(x, y).
Use the distance formula for each given distance:
AE² = (x + 2)² + (y - 5)² = 2²BE² = (x - 2)² + (y - 3)² = 4²CE² = (x + 2)² + (y + 4)² = 7²Use the first and third equations, considering both have same term for x, and solve for y:
(y - 5)² - 4 = (y + 4)² - 49y² - 10y + 25 - 4 = y² + 8y + 16 - 4918y = 54y = 3Substitute y into one of equations and solve for x:
(x + 2)² + (3 - 5)² = 4(x + 2)² + 4 = 4(x + 2)² = 0x + 2 = 0x = - 2The epicenter is E( - 2, 3)
Answer:
(-2, 3)
Step-by-step explanation:
Given:
A = (-2, 5) → 2 miles awayB = (2, 3) → 4 miles awayC = (-2, -4) → 7 miles awayModel each given point as the center of a circle and the distance the epicenter is away from the point as the circle's radius.
The epicenter's location will be the point of intersection of the three circles.
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) is the center and r is the radius
Circle A
center = (-2, 5)radius = 2 miles[tex]\implies (x+2)^2+(y-5)^2=4[/tex]
[tex]\implies x^2+4x+4+y^2-10y+25=4[/tex]
[tex]\implies x^2+4x+y^2-10y+25=0[/tex]
Circle B
center = (2, 3)radius = 4 miles[tex]\implies (x-2)^2+(y-3)^2=16[/tex]
[tex]\implies x^2-4x+4+y^2-6y+9=16[/tex]
[tex]\implies x^2-4x+y^2-6y-3=0[/tex]
Circle C
center = (-2, -4)radius = 7 miles[tex]\implies (x+2)^2+(y+4)^2=49[/tex]
[tex]\implies x^2+4x+4+y^2+8y+16=49[/tex]
[tex]\implies x^2+4x+y^2+8y-29=0[/tex]
To find the point of intersection of the three circles, solve simultaneously.
Substitute equation B into equation A to eliminate x² and y²:
[tex]\implies x^2-4x+y^2-6y-3=x^2+4x+y^2-10y+25[/tex]
[tex]\implies -4x-6y-3=4x-10y+25[/tex]
Rearrange to isolate y:
[tex]\implies -6y-3=8x-10y+25[/tex]
[tex]\implies 4y-3=8x+25[/tex]
[tex]\implies 4y=8x+28[/tex]
[tex]\implies y=2x+7[/tex]
Substitute the expression for y into equation C and simplify:
[tex]\implies x^2+4x+(2x+7)^2+8(2x+7)-29=0[/tex]
[tex]\implies x^2+4x+4x^2+28x+49+16x+56-29=0[/tex]
[tex]\implies 5x^2+48x+76=0[/tex]
Substitute the expression for y into equation B and simplify:
[tex]\implies x^2-4x+(2x+7)^2-6(2x+7)-3=0[/tex]
[tex]\implies x^2-4x+4x^2+28x+49-12x-42-3=0[/tex]
[tex]\implies 5x^2+12x+4=0[/tex]
Equate the equations to eliminate 5x² and solve for x:
[tex]\implies 5x^2+48x+76=5x^2+12x+4[/tex]
[tex]\implies 48x+76=12x+4[/tex]
[tex]\implies 36x+76=4[/tex]
[tex]\implies 36x=-72[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the found expression for y:
[tex]\implies y=2(-2)+7[/tex]
[tex]\implies y=-4+7[/tex]
[tex]\implies y=3[/tex]
Therefore, the point of intersection of the three circles if (-2, 3) and hence the location of the earthquake's epicenter is (-2, 3).
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WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
What is a Square?A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square
Step-by-step explanation:
so its c for me
If DAB = 80°, then DAC =
Answer:
80
Step-by-step explanation:
DAB =DAC...........
Kylie has a modern quarter with a mass of 5.623 g and an older silver quarter with a mass of 6.24 g What is the combined mass of the quarters?
Answer:
11.863 g
Step-by-step explanation:
5.623 g + 6.24 g = 11.863 g
a. If you wanted to draw a circle around this triangle that passed through points A, B, and C as shown by circle P, what steps would you take to do that? b. What steps would you take to draw a circle within the triangle such that each side of the triangle became a tangent line to the circle as shown by circle R? c. If a line drawn from point B to point P measures 2 inches, what is the diameter, circumference, and area of circle P in terms of I? d. Describe how you would find the area of the region bounded by segment BC and arc BDC in terms of a if the arc measure of arc BDC is 60°
The circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
Steps involved in inscribing a triangleThe steps involved in inscribing a triangle;
Construct two chords on the circle.Then , draw a perpendicular bisector to the chords with the compass which must meet at the center of the circle. Make a line from the center to one of the farthest points of the chords.Draw two lines to form a 30 degree with the radius on the opposite side.Stretch out these two lines to make two chords on the circle. The two chords should make angle of 60 degrees to each other.Then connect the other extreme of the two chords this makes an equilateral triangle.If the line drawn from point B to point P measures 2 inches, then the diameter is
= 2 × 2
= 4 inches.
The formula for calculating the circumference of a circle is given as;
Circumference = 2 π r
Radius = diameter/ 2
Radius = 4/2 = 2 Inches
Substitute the values
Circumference = 2 × 3. 142 × 2
Circumference = 12. 57 inches
Area = π r²
Area = 3. 142 × 2²
Area = 3. 142 × 4
Area = 12. 57 square inches
Thus, the circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
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find the volume of the solid generated by rotating the
region bounded by the curves y=0, y= (x^2)+x, x=2
and x=0 about the y-axis
The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.
How to find the volume of the solid generated?To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.
So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]
Now given that the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.
So, we integrate from x = 0 to x = 2.
[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]
[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]
So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.
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Which of the relations given by the following sets of ordered pairs is a function?
O {(2,-8), (1, — 4), (0, 0), (1, 4), (2, 8)}
O {(3, -3), (3, -1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(-2,5), (7,5), (-4, 0), (3, 0), (1, -6)}
Answer:
Option (4)
Step-by-step explanation:
Each value of x maps onto only one value of y, so it is a function.
The margin of sampling error is obtained by multiplying the standard error with the _______.
The margin of sampling error is obtained by multiplying the standard error with the critical value.
What is the margin of sampling error?
The margin of sampling error is a statistic that tells a researcher by how many percentage points the result gotten from the sample value would differ from that of the population. This value is obtained by multiplying the standard error with the critical value.
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Which ordered pair is a solution to the inequality 3x-4y<12 ?
The ordered pair (2,-1) is a solution the inequality.
Given the inequality is 3x-4y<12.
An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.
By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.
1. (4,0)
Here x=4 and y=0
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(0)<12
12<12
This is not true
2. (0,-3)
Here x=3 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(0)-4(-3)<12
12<12
This is not true.
3. (2,-1)
Here x=2 and y=-1
Substitute this in the inequality 3x-4y<12, we get
3(2)-4(-1)<12
6+4<12
10<12
This is true.
4. (4,-3)
Here x=4 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(-3)<12
12+12<12
24<12
This is not true.
Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).
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Match the expressions to their solutions or equivalents. (-3/8) + (-1/8)
Answer:
-1/2
Step-by-step explanation:
-3/8+-1/8=-4/8 which is equal to -1/2
Answer:
1/4
Step-by-step explanation:
(3/8)+(-1/8)
= (3/8) - (1/8)
= 2/8
= 1/4
The sun
of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
The Third would be 72
Step-by-step explanation:
The sum of the two is 16+22=38. the third one is 72-38=34
A file that is 273 megabytes is being downloaded. If the download is 18.9 complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
51.6 megabytes
Step-by-step explanation:
It is asking you what 18.9 percent of 273 is. To find this you multiply 18.9 x 273 and then divide it by 100 which equals 51.597.
You then round it to the nearest tenths which gives you 51.6
find the outer perimeter of this figure
Answer:
41.12 ft
Step-by-step explanation:
10 + 6 = 16
2 x pi x r = 25.12
16 + 25.12 = 41.12
Answer:
Step-by-step explanation:
find the outer perimeter of this figure
we find the perimeter of the semicircleThe perimeter of circle formula = 2πr unitsr = diameter : 2 = 8 : 2 = 4
2π4 =
8π=
8 × 3.14 = 25.12 ft
find figure perimeter
25.12 + 6 + 10 =
41.12 ft
Solve.
Three times the sum of some number plus 3 is equal to 7 times the number minus 23.
The unknown number of the given expression is 8
Linear equationsLet the unknown number be x such that three times the sum of some number plus 3 is equal to 7 times the number minus 23 is expressed as;
3(x + 3) = 7x - 23
Expand
3x + 9= 7x - 23
Collect the like terms
3x-7x = -23 - 9
-4x = -32
x = 8
Hence the unknown number of the given expression is 8
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Consider the following graph
a) What is the equation of the axis?
b) What is the period?
c) What is the amplitude?
d) Is this a sine graph or a cosine graph? Explain
a) The equation of axis is the middle y-coordinate, which is y = -1.5.
b) The period is the amount of time it takes for the graph to repeat, which is 6.
c) The amplitude is the vertical distance from an extreme point to the midpoint, which is 3.
d) This is a cosine graph since when x=0, y is not equal to 0.
11. What effect size do you use for parametric t-tests?
12. What effect size do you use for non-parametric t-tests?
13. What effect size would you use for chi-square tests?
The effective sizes for parametric tests, non parametric tests and chi square tests are as detailed below.
How to interpret the size of statistics test?
11) Parametric t-tests are statistical tests that assume the data approximately follows a normal distribution. Now, when trying to check for parametric t-tests, the effective size we use is Cohen's d which is an appropriate effect size for the comparison between two means.
12) Nonparametric t-tests are those statistical tests that don’t assume anything about the distribution followed by the data, and hence are also known as distribution free tests.
In non - parametric t - tests, we calculate effect size by using the formula;
r = z/√N
where;
r is effect size
z is z value
N is Observation number.
13) In the chi-square test, the effect size index (w) is calculated by dividing the chi-square value by the number of scores and taking the square root.
The effective size is considered small if w = 0.10, Considered medium if w = 0.30, and large if w = 0.50.
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Sheffield corporation shipped $20400 of merchandise on a consignment to Gooch company. Sheffield paid frieght cost of $2000. Gooch company paid $480 for local advertising wich is reimbursed from Sheffield . By year end 62% of the merchandise had been sold for $21500.Gooch notified Sheffield , retained a 10% commission , and remitted the cash due Sheffield . Prepare sheffield journal entry when the cash is received
The appropriate journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.
Journal entrySheffield corporation entries
Debit Cash $18,870
[$21500-($480+ ($21500×10%))]
Debit Advertising expense $480
Debit Commission expense $2,150
(21,500×10%)
Credit Revenue from consignment sales $21,500
Debit Cost of goods sold $13,888
[($20400+$2000)×62%]
Credit Inventory on consignment $13,888
Therefore journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.
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2x+9=1x-5 what is x?
Answer:
2x+9=1x-5
2x-1x=-5-9
x=-14
I need help with this slope
Answer:
B, C
Step-by-step explanation:
Look at the lower blue point.
Its coordinates are (4, 3).
The x-coordinate, 4, stands for minutes.
The y-coordinate, 3, stands for number of boxes.
This is a slope of 3/4, corresponding to 0.75 boxes per minute, or 3 boxes every 4 minutes.
Answer: B, C
Answer:
3 boxes are filled every 4 minutes.
Step-by-step explanation:
Look at the graph; at the bottom of the graph, it is shown that every __ minutes, __ boxes are filled. If you look at the first shown blue point on the left of the graph, it shows that on the fourth minute, three boxes are filled, as from the axis, you go right four and up three.