The answer is 16 1/6
Step-by-step explanation:
1. make both of the denominators into six : 1/2=3/6 and 2/3=4/6
2. add them all together 8+7=15, 4/6+3/6=7/6
3. make the 7/6 into a mixed number so 1 1/6 add that to the 15 so 16 1/6
Answer: 16 1/6
To add mixed numbers, the first thing you do is convert the mixed numbers into improper fractions. How?
You multiply the whole number with the denominator of the proper fraction, then you'll add the numerator.
First mixed number is 8 1/2.
So, you'll multiply 8 by 2 then add 1.
(8 × 2) + 1 = 17
Next is 7 2/3.
Repeat this process.
(7 × 3) + 2 = 23
When your done, plug in the denominator and find the LCD, since the denominators are unlike. (First find the LCM of 2 and 3, which is 6). Our improper fractions should be:
8 1/2 = 17/2 × 3/3
7 2/3 = 23/3 × 2/2
Multiply the LCD, which is 2 and 3 and you'll get:
LCD of 8 1/2 ⇒ 51/6
LCD of 7 2/3 ⇒ 46/6
Now we can add. (You DO NOT add the denominator).
51/6 + 46/6 = 97/6
Since 97/6 is an improper fraction, we must convert it into a whole number.
Divide 97/6 and you'll get 16 with a reminder of 1.
16 is the whole number.
1 is the numerator.
Hence, the answer is 16 1/6.
A couple stayed for 3 years before having their first child. then 2 years before the second. 2 years again before the third, and so on until the sixth child. If the husband was 28 years and the wife was 25 years when they had their first child, what is the sum of the ages of the couple a year before the last born?
Answer:
71
Step-by-step explanation:
25+2+2+2+2+1=34
28+2+2+2+2+1=37
sum=34+37
71
Answer:
3+2+2=7 year back
28-7=21
25-7=18
years old pls mark me as brainlist
Isosceles triangle has , and a circle with radius is tangent to line at and to line at . What is the area of the circle that passes through vertices , , and
The circle that passes through the vertices of triangle ΔABC (A, B, C) is the
circumscribing circle of triangle ΔABC.
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Reasons:
The given parameters are;
Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6
Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2
Required:
Area of the circle that passes through vertices A, B, and C
Solution:
Angle ∠BAO is given as follows;
[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]
∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')
[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
From sine rule, we have;
[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]
Using a graphing calculator, we get;
[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]
The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)
Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Learn more here:
https://brainly.com/question/17147358
The possible question options obtained from a similar question online are;
(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π
b. 2x^2 + 15 _<13x solve polynomial inequality by factoring.
Answer:
x<5 or x<3/2
Step-by-step explanation:
2[tex]x^{2}[/tex]-13x+15<0
2[tex]x^{2}[/tex]-10x-3x+15<0
2x(x-5)-3(x-5)<0
(x-5)(2x-3)<0
x-5<0 or 2x-3<0
x<5 or x<3/2
The product of two positive odd consecutive integers is 1599. What is the larger integer?
Answer:
800
Step-by-step explanation:
800+799=1599
Solve them ALL... BWAHAHAHAHAHAHAHAHAHAHAHAHAHAHA. Anyway Good LUCK
the first one is (B) i think
the second one is (B)
the third one is (B)
the fourth one is (A)
the fifth one is (A)
Find the measure of each interior angle of a polygon having 9 sides
Answer:
Sum of the interior angles = 1260°.
Step-by-step explanation:
Sum of the interior angles = (n - 2)180° where n= number of sides
Sum of the interior angles = (9-2)180
Sum of the interior angles = 1260°
9.091 as a mixed number
Se construye cubo de madera de qué tiene 26 m de aristas y se debe cubrir todo el cubo con plástico cuántos metros cuadrados de plástico se necesitará
Answer:
i tink its a
Step-by-step explanation:
(28 ⋅ 5−5 ⋅ 190)−2 ⋅ 5 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 228. Help.
Answer 5-5.190 =-945 -2=-947 2-2=0+3 =3+7=-935
Step-by-step explanation:
A long-sleeve shirt has 8 front buttons and 2 cuff buttons; a short-sleeve shirt has 6 front buttons and no cuff buttons. The factory which makes ‘Slimboy Shirts’ uses 10 times as many front buttons as cuff buttons. What is the ratio of long-sleeve shirts to short-sleeve shirts produced by the factory?
Leave your ratio in its simplest form.
Answer:
ratio of long-sleeved shirts to short-sleeved shirts is 1:2 this is my answer that I thought of if you don't feel comfortable believing me just wait for another person to answer and see what they say.
Step-by-step explanation:
Find the equation of the line.
Answer:
Step-by-step explanation:
(-4,-5) and (6,4)
Slope: (4 - - 5) / ( 6 - - 4) = 9/10
y-intercept= - 5 - (9/10)(-4)
= - 5 + 36/10 = -7/5
y = 9/10x - 7/5
The equation of the line is x + 10y -19 = 0.
We are given that;
The points of line segment= (6,4) and (-4,5)
Now,
To find the equation of a line given two points, we can use the two-point form formula:
y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1)
where (x 1, y 1) and (x 2, y 2) are the two given points and (x, y) is any point on the line.
We have:
(x 1, y 1) = (6,4)
(x 2, y 2) = (-4,5)
Substituting these values into the formula, we get:
y − 4 = 5 − 4 -4 − 6 ( x − 6)
Simplifying and rearranging, we get:
y = -1/10 x + 19/10
This is the equation of the line in slope-intercept form. We can also write it in standard form by multiplying both sides by 10 and moving all terms to one side:
x + 10y -19 = 0
Therefore, by equation the answer will be x + 10y -19 = 0.
Learn more about equation;
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Please help if you can I'll even give you a brainiest answer.
Find the equation of the line.
Answer:
y= 4/1x +1
Step-by-step explanation:
the number on the y axis is the b and you do rise over run to find m you rise (so you go up or down) 4 times and run( go to the sides) once.
rise 4
-------- = -----
run 1
Answer:
y = 3x + 1
Step-by-step explanation:
Slope: As it rises 3, it runs 1
Slope = Change in y/change in x
Slope = 3/1
y - intercept = 1 ,the point of intersection
Equation : y = mx + b
m = slope
b = y-intercept
Equation : y = 3x + 1
-Chetan K
Solve for x:
Yeah can't come in3x+7x=10x
Answer:
#happy learningStep-by-step explanation:
#brainly phConsider this expression x^2-(3x+y)+16
Answer:
x^2-3x-y+16?
Step-by-step explanation:
simplest form already, but can be converted into a proper polynomial.
x^2-3x-y+16
Please Help!! I can"t solve this ! Kendrick had 2/3 of an ice cream cake left. Each piece on the ice cream cake is 1/ 12 of the entire cake. How many pieces are left?
Answer:
8
Step-by-step explanation:
Anyone know the answer to this plz
Answer:
Domain: -10 < x < 10
Range: -2 < y < 8
Step-by-step explanation:
Hope this helps!
19. Round the number 347 500 to the nearest 1000; 10 000 and 100 000.
To the nearest 1000
To the nearest 10 000
To the nearest 100 000
Answer:
34800, 350000, 300000
Step-by-step explanation:
5>=5
34800
7>=5
350000
4<=5
300000
Solve the equation for y. 5x+2Y=9
Answer:
y = 9/2 - 5/2(x)
Step-by-step explanation:
I think this is right
find the value of x for which f(x)=4
[tex] \: \: \: [/tex]
[tex]f(x) = 4[/tex]
The domain of a constant function is the set of all real numbers[tex]x = R[/tex]
hope it helps[tex] \: \: \: [/tex]
Sales commissions: A company studied two programs for compensating its sales staff. Nine salespeople participated in the study. In program , salespeople were paid a higher salary, plus a small commission for each item they sold. In program , they were paid a lower salary with a larger commission. Following are the amounts sold, in thousands of dollars, for each salesperson on each program
Salesperson
Program 1 2 3 4 5 6 7 8 9
A 55 22 34 22 25 61 55 36 68
B 53 24 36 28 31 61 58 38 72
Required:
Can you conclude that the mean sales differ between the two programs? Use the α = 0.05 level of significance
Using the t-distribution, it is found that since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.
At the null hypothesis, it is tested if the mean sales do not differ between the two programs, that is, the subtraction of the means is 0, hence:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if they differ, that is:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The mean and the standard errors for each sample are:
[tex]\mu_1 = 42, s_1 = 5.9675[/tex]
[tex]\mu_2 = 44.56, s_2 = 5.6177[/tex]
The distribution of the difference has mean and standard deviation given by:
[tex]\overline{x} = \mu_2 - \mu_1 = 44.56 - 42 = 2.56[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{5.9675^2 + 5.6177^2} = 8.1957[/tex]
The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]t = \frac{2.56 - 0}{8.1957}[/tex]
[tex]t = 0.31[/tex]
The critical value for a two-tailed test, as we are testing if the mean is different of a value, with 9 + 9 - 2 = 16 df and a significance level of 0.05 is [tex]|t^{\ast}| = 2.12[/tex]
Since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.
A similar problem is given at https://brainly.com/question/13873630
A. 48 inches
B. 4 feet
Explain why length A is equivalent to length B. Use your knowledge of converting inches to feet in your answer.
Answer:
As 1 feet = 12 inches
Therefore, 4 feet = 48/12
= 4
Answer = 4 feet
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
A Subchapter S corporation:
is similar to a partnership in that it carries unlimited liability.
is a separate legal entity which is treated like a normal corporation.
has all the organizational benefits of a corporation and its income is only taxed once.
all of the above.
describe these sets 2,4,8,16,32,64
Answer: They are all divisible by 2.
Step-by-step explanation: They all have 2 in common. If you divide them by 2, they all work. Also, if you simplify all to the lowest number, they equal 2 except 2 itself which equals 1.
Answer:
divisible by 2 luv
Step-by-step explanation:
How do you find the answer for 30=6x+20
Answer:
5/4Step-by-step explanation:
How do you find the answer for 30=6x+20?
solve for x30 = 6x + 20
10 = 6x
x = 10/6
semplify5/4
------------------ check
30 = 6 * 10/6 + 20
30 = 10 + 20
30 = 30
the answer is good
What is the distance between the two points (-7, -7) and (4, -3)?
a. 5
C. 10.44
b. 7
d. 11.7
Please select the best answer from the choices provided
This diagram models 3 friends who are sharing 2 turkey sandwiches equally.
How much does each friend get?
1/3 sandwich
2/3 sandwich
11/3 sandwiches
11/2 sandwiches
Answer:
2/3 sandwich.
Step-by-step explanation:
No Explanation
Find the difference:
x+
x-1
-
- 8
x-1
O
9
x-1
2-7
X1
-7
1
2x+9
1
DONE
Answer: [tex]\frac{9}{x-1}[/tex]
Step-by-step explanation:
Since the denominators are the same, we can subtract the numerators.
[tex]\frac{x+1}{x-1}-\frac{x-8}{x-1}=\frac{(x+1)-(x-8)}{x-1}=\boxed{\frac{9}{x-1}}[/tex]
A game designer is creating a computer animation of a rectangle with sides that vary in size. The length of the rectangle in centimeters after t seconds is given by the expression 2t-9, while the width is given by the expression 1 + t. After how many seconds is the rectangle a square?
Answer:
Step-by-step explanation:
Squares have equal length and widths
2t - 9 = 1 + t
2t - t - 9 + 9 = 1 + 9 + t - t
t = 10 s
???????????????????? :((
Step-by-step explanation:
1. Not all rational numbers are whole numbers. Whole numbers can be rational numbers, if expressed in fraction form. For example, 1 can be expressed as [tex]\frac{1}{1}[/tex]. A set of rational numbers consists of a set of numbers written as a quotient of two integers, a and b, in the form [tex]\frac{a}{b}[/tex] , where b ≠ 0. The reason why b ≠ 0 because division by zero is an undefined mathematical operation.
2. Irrational numbers differ from rational numbers in terms of its representation: while the rational numbers can be expressed as a ratio or in fraction form, irrational numbers cannot be expressed in fraction form.
Irrational numbers are a set of numbers for which its decimal representations is neither terminating, nor repeating. A couple examples of irrational numbers are: π and [tex]\sqrt{2}[/tex], as their decimal representations do not come to an end and doesn't have a block of repeating digits.
3. All real numbers are rational numbers. Real numbers comprise of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.