Answer:
14 years 7 months
Step-by-step explanation:
If the average age was increased by 2 months by adding a 7th child, the total age was increased by 2·7 months = 14 months more than the previous average. That is, the added child's age is 14 months more than the previous average, so is ...
... (13 years + 5 months) + (1 year + 2 months) = 14 years + 7 months
_____
For the non-believers:
The previous total of all ages was ...
... 6 × (13 years 5 months) = 80 years 6 months
The new total of all ages is ...
... 7 × (13 years 7 months) = 95 years 1 month
The amount added to the previous total is ...
... (95 1/12 - 80 6/12) years = 14 7/12 years = 14 years 7 months
To find the age of the seventh child, calculate the total age of the six children and the total age of all seven children.
Explanation:To solve this problem, we can use the concept of the average. Step 1: Calculate the total age of the six children by multiplying the average age (13 years and 5 months) by the number of children (6). Step 2: Calculate the total age of all seven children by multiplying the new average age (13 years and 7 months) by the total number of children (7). Step 3: Subtract the total age of the six children from the total age of all seven children to find the age of the seventh child.
Learn more about Average age here:https://brainly.com/question/35710268
#SPJ2
Which equations could you use to solve the following problem? Fifty-six is 85% of what number? 56 = (0.85)w = = p = (0.85)56
Answer:
56 = (0.85)w
Step-by-step explanation:
"is" translates to "=".
"of" translates to "×".
We can let "what number" translate to "w".
Then ...
56 is 85% of what number . . . . translates to ...
56 = 0.85×w
_____
Of course, you know that 85% = 85/100 = 0.85.
if point p is 3/8 of the distance from a to b, then point p partitions the directed line segment into what ratio from a to b? a. 3:11 b. 8:11 c. 3:5 d. 5:3
Answer:
b
Step-by-step explanation:
Final answer:
Point P divides the distance from A to B into a ratio of 3:5, with P being 3/8 of the way from A to B. The correct option is c.
Explanation:
If point P is 3/8 of the distance from A to B, we can understand this situation by imagining the entire distance from A to B as being divided into 8 equal parts, and point P lies at the end of the third part when moving from A to B. Since P is 3 parts away from A, it leaves the remaining 5 parts to reach B. This sets up a partition of the segment into two parts: one from A to P and the other from P to B. The ratio of these distances is the number of parts from A to P to the number of parts from P to B. Therefore, the ratio of AP to PB is 3:5. Option c is accurate.
The measure of one of the angles formed by two parallel lines and a transversal is 45°. Is it possible for the measure of any of the other seven angles to be equal to 55°? Explain.
Answer: No
Step-by-step explanation:
Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.
Convert to rectangular form.
Answer:
-16 sqrt(3) +16i
Step-by-step explanation:
z = 2 cis (pi/6)
z^5 = 2^5 cis (5*pi/6)
z^5 = 32 cis (5pi/6)
z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)
= 32 * (-sqrt(3)/2) + 32i (1/2)
= -16 sqrt(3) +16i
A point on the rim of a wheel moves with speed of 200 feet per second. Find the angular velocity of the point if the diameter of the wheel is 8 feet.
The angular velocity of the point is found this way:
w = v/r
w = 200/(8/2) <--the two is from 2 * Pi * r
w = 50 rad/sec.
Answer: 50 rad/sec.
fullness; live
a park plants youn maple trees.a maple tree grows the rate of 1 1/2 feet per year how tall will the tree be in 20 years
Answer:
it will grow 30 ft in 20 years
Step-by-step explanation:
the height will equal the growth rate times the time
height = 1.5 ft/year * 20 year
height = 30 ft
Which sequence matches the recursive formula? an=2an-1+5, where a1=5. A) 5,10,15,20 B) 5,15,35,75. C)5,15,25,35. D) 5,20,35,40
The recursive formula
[tex] a_n = 2a_{n-1}+5 [/tex]
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]
Next, we will double 15 and add 5:
[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]
Which confirms option B
What is the Value of x+y ? PLZ Help ASAP
Answer:
x + y = 60
Step-by-step explanation:
In the given figure, we have two lines that intersect each other at one point.
Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:
2y - 5 = 95 --- (1)
3x + 55 = 85 --- (2)
Now solving each of the equations to find the value of x and y.
For y:
2y - 5 = 95
2y = 95 + 5
2y = 100
y = 50
For x:
3x + 55 = 85
3x = 85 -55
3x = 30
x = 10
Therefore, x + y = 10 + 50 = 60.
The sides of a square are two to the power of four-ninths inches long. What is the area of the square?
two to the power of the fraction sixteen over eighty-one square inches
four to the power of the fraction sixteen over eighty-one square inches
two to the power of eight-ninths square inches
four to the power of eight-ninths square inches
Answer:
2^(8/9) in²
Step-by-step explanation:
Make use of the identity ...
... (a^b)^c = a^(bc)
Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity
... (ab)^c = a^c·b^c
In this case a = 2^(4/9), b = in, c = 2.
So, the working of your problem is ...
... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2
... = 2^(4/9·2) in^2 = 2^(8/9) in^2
The length of the rectangle is 7 inches, the width is w inches. If the coefficient of the width increases by 3, what could be an expression for the area of the rectangle?
Answer:
A = 10w
Step-by-step explanation:
In the area formula, the coefficient of width is length. Here, that is ...
... A = 7w
7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...
... A' = 10w
_____
Comment on the problem statement
The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.
Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.
At a high school with 800 students, 80% of the students ride the school bus. if 20 students are selected randomly (without replacement) and we let x = the number of students in the sample who ride the bus, what is the probability that at least one of the students doesn't ride the bus?
Answer:
0.9885 (98.85%)
Step-by-step explanation:
Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.
So we want to calculate P( X < 20 ).
We can calculate the probability of complement event P( X = 20 ).
Use binomial formula b(x; n, p) = C( n, x ) p^(x) (1-p)^(n-x)
b( 20; 20, 0.8 )
= C( 20, 20 ) (0.8)^(20) (0.2)^0
= (0.8)^20 ≈ 0.0115
So since P( X < 20 ) = 1 - P( X = 20 ), we have
P( X < 20 ) ≈ 1 - 0.0115 = 0.9885
The required value of probability for the given sample is given as 0.9885.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Total number of students are given as 800.
The probability of students riding the school bus is 80% = 0.8.
Then, probability of students not riding the school bus is 1 - 0.8 = 0.2.
The probability of finding at least one student out of 20 not riding the bus is given as,
1 - P(All of the students ride bus)
It can be solved using binomial distribution as follows,
⇒ 1 - ²⁰C₂₀(0.8)²⁰(0.2)⁰
⇒ 1 - 0.0115 = 0.9885
Hence, the probability that at least one of the students doesn't ride the bus is given as 0.9885.
To know more about binomial distribution click on,
https://brainly.com/question/14565246
#SPJ5
Which pair of numbers is relatively prime?
A. 12 and 54
B. 9 and 21
C. 21 and 39
D. 15 and 49
Answer:
D. 15 and 49
Step-by-step explanation:
Numbers are relatively prime if the only positive integer that divides both of them is 1.
A. 12 and 54
both 12 and 54 can be divided by 3
12/3 =4 54/3 = 18
B. 9 and 21
both 9 and 21 can be divided by 3
9/3 =3 and 21/3 = 7
C. 21 and 39
both 21 and 39 can be divided by 3
21/3 =7 and 39/3 = 13
D. 15 and 49
13 is 3*5 and 49 is 7*7
This is relatively prime
Is the simplified form of 2 square root of 3 ⋅ square root of 12 rational?
Yes
No
Answer:
It is rational
Step-by-step explanation:
2 * sqrt(3) * sqrt(12)
2 * sqrt(3) sqrt(4) * sqrt(3)
2 sqrt(3) 2 sqrt(3)
4 sqrt(3)^2
4 *3
12
If P(3,2) and Q(7,10) are the endpoints of the diameter of a circle, what is the area of the circle in square units?
To find the area of a circle given its diameter's endpoints, determine the diameter length, radius, and then calculate the circle's area using the radius.
Explanation:The area of a circle can be found using the distance formula between two points representing the diameter's endpoints. Given points P(3,2) and Q(7,10), the diameter length is calculated as sqrt((7-3)^2 + (10-2)^2) = sqrt(4^2 + 8^2) = sqrt(16+64) = sqrt(80).
Knowing that the radius is half the diameter, the radius, r = sqrt(80)/2 = 4*sqrt(5).
Finally, the area of the circle is A = pi*r^2 = pi*(4*sqrt(5))^2 = 80*pi square units.
What common side do AEG and ADE have
Answer:
AE
Step-by-step explanation:
Pairs of letters identify line segments:
... AE, EG, AG
... AD, DE, AE
Segment AE is common to both lists.
i need help on finding the orthocenter of a triangle, i got the x right, x=6 but I got the Y value wrong, it's supposed to be y=4 but i got y=8 as my answer. the question is find the coordinates of the orthocenter of Triangle ABC with vertices A(2,6), B(8,6), and C(6,2). what i did to find the Y value was find the slope of BC then use that value and the coordinates of A and substituted them into an equation y-6=1/2(x-2), i solved it and got y = 1/2x+5. i then substituted my x value that i previously found into it to find Y , y=1/2(6)+5 . i got 8 as the Y value but it's wrong, can someone tell me what i missed?
Answer:
See the attached
Step-by-step explanation:
When in doubt, draw a diagram.
The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.
The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.
The perpendicular line to BC through A is ...
... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)
The intersection of that line and x=6 is ...
... y = -6/2 +7 = 4
find each side length. Round to the nearest tenth if necessary
x = 8.5
The other two sides are given in the diagram.
Step-by-step explanation:The Pythagorean theorem tells you ...
... 19² = 17² +x²
Subtracting 17², we have ...
... x² = 361 -289 = 72
Taking the square root gives x.
... x = √72 = 6√2
... x ≈ 8.5
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
2
Step-by-step explanation:Solve the second equation for y.
... 8x -12 = 4y . . . . add 4y -12
... 2x -3 = y . . . . . . divide by the coefficient of y
The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...
... y = 2x -6 . . . . . . . . m = 2
will be parallel to the given line, so will not intersect it.
Help asap I need help with these questions i have to show work too.
Answer:
1: Simplify 15/20 to 3/4
y/4=3/4
Multiply both sides by 4
y=3/4×4
Simplify 3/4×4 to 12/4
y=12/4
Simplify 12/4 to 3
y=3
2: Multiply both sides by z-3
6=8/5(z-3)
Simplify 8/5(z-3) to 8(z-3)/5
8(z-3)/5
Multiply both sides by 5
6×5=8(z-3)
Simplify 6×5 to 30
30=8(z-3)
Divide both sides by 8
30/8=z-3
Simplify 30/8 to 15/4
15/4=z-3
Add 3 to both sides
15/4+3=z
Simplify 15/4+3 to 27/4
27/4=z Switch sides z=27/4
Sarah and her brother are 6 years apart. Right now, the ratio of their ages is 3:4. How old are both of them right now?
Sarah: 18
Brother: 24
Step-by-step explanation:The difference in ratio units is 4-3 =1. The difference in years is 6, so 1 ratio unit stands for 6 years.
Multiplying by 6, we have ...
... Sarah : Brother = 3·6 : 4·6 = 18 : 24
Sarah is 18; her brother is 24.
someone help pleaseeesee
Answer:
A. 36°
Step-by-step explanation:
Same-length chords subtend same-measure arcs. Arc YZ has the same measure as its central angle (∠YOZ) and the same measure as arc XY (36°).
the measure of angle YOZ is 36°, which corresponds to option A. Therefore, the correct answer is option b.
The measure of an angle formed by two chords in a circle is half the measure of the arc intercepted by the angle.
If chord XY is congruent to chord YZ, it means that the arcs intercepted by these chords are also congruent.
So, if the measure of arc XY is "x" degrees, then the measure of arc YZ is also "x" degrees.
Now, the angle YOZ is formed by these two congruent arcs. Therefore, the measure of angle YOZ is half the measure of the arcs XY and YZ.
Angle YOZ = 0.5 * (x + x) = 0.5 * 2x = x degrees.
Now, if you're given the measure of arc XY (or YZ), you can substitute that value into the formula to find the measure of angle YOZ.
The answer choices you provided are in degrees, so the correct answer is A. 36°, assuming you have the measure of the arc XY (or YZ) in the problem.
Learn more about Measure of angle YOZ here:
https://brainly.com/question/29205120
#SPJ3
Question: Which of the following represents the equation of a line that is parallel to the line r shown in the graph?
Answer:
B
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1,1) ← 2 points on the line
m = [tex]\frac{1+1}{1+1}[/tex] = 1 ← slope of graph
consider the slope of the given equations
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(A)
y = 2x + 1 has slope = 2 → not parallel
(B)
x - y = - 3 ( subtract x from both sides )
- y = - x - 3 ( multiply through by - 1 )
y = x + 3 with slope = 1 → thus parallel to graph
(C)
x + y = 2 ( subtract x from both sides )
y = - x + 2 with slope = - 1 → not parallel
(D)
y = - x + 1 with slope = - 1 → not parallel
An equation of a line that is parallel to the line r shown in the graph include the following: B. x - y = -3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope for this line by using these points (1, 1) and (0, 0);
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope (m) = (0 - 1)/(0 - 1)
Slope (m) = 1
For the line to be parallel to the line r, it must have the same slope as line r. At data point (0, 0) and a slope of 1, an equation for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
y - 0 = 1(x - 0)
y = x
Based on the answer options, we have;
y = 2x + 1 ⇒ slope is 2 (not parallel).
x - y = -3
y = x + 3 ⇒ slope is 1 (parallel).
Read more on point-slope here: brainly.com/question/24907633
#SPJ3
5.5 oz = __________ kg
Answer:
0.155922
Step-by-step explanation:
Answer: 0.1562 kilograms
Step-by-step explanation: To convert 5.5 ounces into kilograms, we first convert 5.5 ounces into grams using the conversion factor 1 oz = 28.4 g.
Since we are going from a larger unit "ounces" to a smaller unit "grams" we multiply 5.5 by the conversion factor which is 28.4 to get 156.2.
This means that 5.5 ounces is equal to 156.2 grams.
Next, we convert 156.2 grams into kilograms using the conversion factor
1 kilogram = 1,000 grams. Since we are going from a smaller unit "grams" to a
larger unit "kilograms" we divide 156.2 by the conversion factor which is 1,000
and we get 0.1562 kilograms.
Therefore, 5.5 ounces is equal to approximately 0.1562 kilograms.
Find the missing values for the exponential function represented by the table below.
x y
-2 4
-1 6
0 9
1 ?
2 ?
a. -13.5 -20.25
b. -13.5 20.25
c. 6 4
d. 13.5 20.25
Answer: D
Answer:
d. 13.5, 20.25
Step-by-step explanation:
An exponential function is monotonic and does not change sign. On this basis alone, the first three choices can be eliminated.
The common ratio is 6/4 = 3/2.
The term in the sequence after 9 is 9·(3/2) = 27/2 = 13.5.
The term in the sequence after 27/2 is (27/2)·(3/2) = 81/4 = 20.25.
Final answer:
The missing values for the exponential function table with an increasing common factor of 1.5 are 13.5 for x=1 and 20.25 for x=2, making the correct answer Option D.
Explanation:
The student's question pertains to finding the missing values for the exponential function represented by the table with given x and y values. Given the nature of an exponential function, we expect that as x increases by 1, the value of y is multiplied by the same factor each time. We can observe this behavior in the initial y-values: 4, 6, and 9. To find this constant multiplier, we can divide 6 by 4 and 9 by 6, which both give us 1.5. This constant factor, which we'll call base of the exponential function, indicates that for every increase of 1 in x, the value of y is multiplied by 1.5.
To find the missing y-values for x=1 and x=2, we just continue multiplying by the base 1.5. Thus, when x=1:
y = 9 × 1.5 = 13.5
When x=2:
y = 13.5 × 1.5 = 20.25
Hence, the completed table should read as follows:
x=-2, y=4
x=-1, y=6
x=0, y=9
x=1, y=13.5
x=2, y=20.25
The correct answer is therefore Option D: 13.5, 20.25.
Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus the square root of 45 end root minus square root of 28
2 square root of 12
2 square root of 2
6 square root of 5 end root minus 4 square root of 7
6 square root of 10 end root minus 4 square root of 14
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}=3\sqrt{5}-2\sqrt{7}+\sqrt{3^2\cdot 5}-\sqrt{2^2\cdot 7}\\\\=(3+3)\sqrt{5}+(-2-2)\sqrt{7}=6\sqrt{5}-4\sqrt{7}[/tex]
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
Answer:
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
simplify
[tex]( \frac{ {h}^{12} }{ {h}^{4} } ) {}^{3} [/tex]
Plz help! and explain how you got the answer
Answer:
[tex]h^{24}[/tex]
Step-by-step explanation:
[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]
When dividing two exponents (of the same bases) you subtract the exponents. When there is an exponent to an exponent, you multiply the to exponents.
[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]
Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race and Jenna had finished 7/12 of the race. Who had finished more of the race?
Final answer:
After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).
Explanation:
Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.
First, let's convert them to decimal form:
2/3 is approximately 0.6667
7/12 is approximately 0.5833
Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.
Lane borrowed $1200 for a new drum set. She will be paying 6.5% in simple interest over the next 2 years. What is the total amount of interest she will be paying on the loan? Show Work
Answer:
Steplo-by-step explanation:loan is 1200.
The interest rate is 6.50
Pp 46.90
Cumulative payment $53.4
Total payments$1,282.93
Final answer:
Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.
Explanation:
Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:
I = PRT
where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.
First, we convert R to a decimal by dividing it by 100:
R = 6.5% / 100 = 0.065
Next, we substitute the values into the formula:
I = $1200 × 0.065 × 2
I = $1200 × 0.13
I = $156
Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.
Four Ice Skaters participate in an ice skating competition. The table shows their scores. Who has the highest score?
Natasha 75.03
Taylor 75.39
Rowena 74.98
Suki 75.3
Answer:
Your answer is Taylor
Step-by-step explanation:
Answer:
Taylor
Step-by-step explanation:
her answer is 0.09 greater then suki who is 2nd biggest
plz mark brainliest
Which table contains a set of non-linear ordered pairs?
Answer:
The table A contains a set of non-linear ordered pairs.
Step-by-step explanation:
To answer this question we have to recall what is the meaning of a linear ordered pair. As you can see, in every table there are 4 values for x, and 4 values for y. In every case, the set of values for x are
[tex]x=\{0, 1, 2, 3\}[/tex]
but in every table, the values for y varies. Now, the key is to calculate the variation of these values, and in order to have a linear relation between x and y, the variation must be the same quantity for every y value that depend of each x value.
For example, in table B, the variation is +3, as from the first y value to the second, 3 is added... and this +3 variation must be the same for each new value of y (and as you can see, 4+3 is 7, 7+3 is 10, 10+3 is 13).
Keeping this in mind, the variation in table C is -2, and the variation in table D is +1, so tables B, C and D contains sets of linear ordered pairs.
To answer the question, we just have to realise that table A has differents variations in the values of y, and this means that it contains a set of non-linear ordered pairs, wich is the correct answer to the question.