Answer:
The 90th term of the arithmetic sequence is 461.
Step-by-step explanation:
Arithmetic sequences concepts:
The general rule of an arithmetic sequence is the following:
[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
In this question:
[tex]a_{1} = 16, d = 21 - 16 = 26 - 21 = 5[/tex]
So
90th term
[tex]a_{90} = a_{1} + (90-1)*d[/tex]
[tex]a_{90} = 16 + 89*5[/tex]
[tex]a_{90} = 461[/tex]
The 90th term of the arithmetic sequence is 461.
how do u do this pls help me understand
Answer:
10.8
Step-by-step explanation:
5 times what gives 6? 5 times 1.2
So now you just do 9 times 1.2 which is 10.8
Answer:
10.8
Step-by-step explanation:
5*x=6
5*1.2=6
9*1.2=r
r=10.8
Dale can type 32 words in 8 minutes.
What is his rate in words per minute?
Answer:4 words per minute.
Step-by-step explanation:32 divided by 8 is 4.
maya was asked whether the following equation is an identity (2x+3)(x+1) = 2(x+1)^2 + (x+1)
Answer:
Maya is correct.
Step-by-step explanation:
Khan Academy gave me the answer.
What is the error in the flow chart
there is no flow chart
Answer:
WHAT FLOWCHART?
Step-by-step explanation:
I need help very urgent
Remember: volume=length x width x height
So i think its 15, 15, and neither of them have greater volume.
Terry has 3 pairs of pants: black, khaki, and brown, and 4 shirts: yellow, red, blue, and white. He does not care which colors he wears together. If Terry chooses one pair of pants and one shirt at random, what is the probability that his outfit will be the black pants with the yellow shirt?
Answer:
1/12 my guy
Step-by-step explanation:
There really isn't one
Answer:
Would be 0.08333 or 1/12
Step-by-step explanation:
can someone please help me ill give a brainliest
Answer:
C
Step-by-step explanation:
-
Answer:
yes
Step-by-step explanation:
The mean weight of females in a class is 60kg and that of the males is 72kg. If the mean
weight of the class is 68kg, what is the ratio of females to males in the class?
Answer:
1:2
Step-by-step explanation:
Let's say there are x males and y females in the class.
The sum of all male weights will be 72x, and the sum of all female weights will be 60y.
If we get a class mean weight, we have:
(72x + 60y) / (x+y) = 68
72x + 60y = 68x + 68y
4x = 8y
y / x = 4/8 = 1/2
So the ratio of females to males is the class is 1:2
Find five rational numbers between 3/7 and 2/3
PLEASE HELP...... I NEED TO SUBMIT THIS NOW....
Answer:
First, you get both of them with same denominator:
3/7 and 2/3 => 9/21 and 14/21, however, there are only 4 rational numbers between 9/21 and 14/21.
The solution is that you can raise the denominator 2 times:
9/21 and 14/21 => 18/42 and 28/42
Now you can select : 19/42, 20/42, 21/42, 22/42, 23/42. They are a group of 5 rational numbers you are looking for.
Trapezoid EFGH is inscribed in a circle, with [tex]EF \parallel GH[/tex]. If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 56 - 3x degrees, where x > 0, find arc EPF, in degrees.
Answer:
Arc EPF is 240°
Step-by-step explanation:
Since the quadrilateral, EFGH is a trapezoid and EF is parallel to GH, we have;
∠HGF + ∠GFE = 180°
∠GHE + ∠GFE = 180°
∠HGF + ∠HEF = 180°
∴∠HEF = ∠GFE
In ΔHEF and ΔGFE
∠EHF = ∠EGF (Angles subtending the same segment)
With side EF common to both triangles and ∠HEF = ∠GFE , we have;
ΔHEF ≅ ΔGFE (Angle Angle Side rule)
Hence, side FG = EH
For cyclic trapezoid side FG = EH
The base angles subtended by GH = 70
Arc EH = x² - 2·x
Arc FG = 56 - 3·x
Therefore;
70 + x² - 2·x + 56 - 3·x + arc EPF = 360 .............(1)
Also since the equation of a circle is (x-h)² + (y-k)² = r², where the center of the circle is (h, k), then as EF is a displacement of say z from GH, then arc EH = FG which gives;
x² - 2·x = 56 - 3·x
x² - 2·x - 56 + 3·x = 0
x² + x - 56 = 0
(x - 7)(x + 8) = 0
Therefore, since x > 0 we have x = 7
Plugging in the value of x into the equation (1), we have
70 + 7² - 2·7 + 56 - 3·7 + arc EPF = 360 .............(1)
70 + 70 + arc EPF = 360
arc EPF = 360 - 140 = 240°.
what is the length of a diagonal of a cube with a side length of 1 cm?
Answer:
sqrt3 or about 1.7
Step-by-step explanation:
length^2 + Width^2 + Height^2 = Diagonal^2
so 1 + 1 + 1 = 3, which when square rooted equals
sqrt3 or about 1.7
Answer:
b
Step-by-step explanation:
edg
Triangle A is a scaled version of triangle B. The dimensions of triangle B are three times the dimensions of triangle A. The area of triangle A is 24.5 sq cm. What is the area of triangle B?
Answer:
The area of triangle B is [tex]2.72cm ^{2}[/tex]
Step-by-step explanation:
We will use the principle of similar triangles to solve the problem.
Since triangle A is just a scale version of triangle B, we can say that the two triangles are similar.
The area scale factor is the square of the length scale factor.
Given the length scale factor as 3,
The area scale factor will be 3 X 3 = 9 sq. cm
(Area of triangle A / Area of triangle B) = (length of side A / Length of side B) square
[tex]\frac{24.5}{ area of B}= 3^{2}[/tex]
[tex]\frac{24.5}{Area of B}= 9\\Area of B = \frac{24.5}{9}= 2.72 cm ^{2}[/tex]
The area of triangle B is [tex]2.72cm ^{2}[/tex]
Grace made a dot plot showing the distances she ran each day for two weeks. She says that she usually runs 7 miles each day because that is the distance that occurs most often. Do you agree with Grace's reasoning?
Answer: No
Step-by-step explanation:
Because Mode is not the best centre of tendency use for statistical data. And mode cannot be used for average.
Mean should be used for average values
Answer:
da ba dee da ba doo im blue
Step-by-step explanation:
Grace made a dot plot showing the distances she ran each day for two weeks.
She says that she usually runs 7 miles each day because that is the distance that occurs most often.
Do you agree with Grace’s reasoning?
Use the drop-down menus to explain and show your answer.
Dot plot named as ALTDCDistances RunALTDC has number line from 1 to 7. 1 dot on 1, 3 dots on 2, 3 dots on 3, 3 dots on 4 and 4 dots on 7 are given.
The mode, which is (3,4, or 7) ,(is or is not) a typical distance for the data. The median, which is (3.5,4, or 7),(is or is not) a typical distance for the data. The mean, which is (3,4, or 7) ,(is or is not) a typical distance for the data. So, Grace’s reasoning(is or is not ) correct.
Factor the expression 2x4y – 18x2y3 completely.
A. 2x2y(x2 – 9y2)
B. 2x2y(x – 3y)(x + 3y)
C. 2x2y(x – 3y)2
D. 2x2y(x – 9y)(x + 2y)
Answer:
B
Step-by-step explanation:
[tex]2x^{4}y - 18x^{2}y^{3}[/tex]
Both sides have [tex]x^{2}[/tex]
[tex]x^{2} (2x^{2}y - 18y^{3})[/tex]
Both sides have y
[tex]yx^{2} (2x^{2} - 18y^{2})[/tex]
Both sides have 2
[tex]2yx^{2} (x^{2} - 9y^{2})[/tex]
Rule : [tex]x^{2} - y^{2} = (x+y)(x -y)[/tex][tex]x^{2} = x.x\\9y^{2} = 3y. 3y[/tex]
[tex](x^{2} - 9y^{2}) = (x +3y) (x-3y)[/tex]
Final:
[tex]\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}[/tex]
Hope this helps ^-^
The factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
What is Factorization?The act of expressing a number or other mathematical object as the sum of numerous factors is known as factorization.
The given expression is 2x⁴y-18x²y³.
Factor the expression as follows:
2x⁴y-18x²y³
= 2x²y(x² - 9y²)
= 2x²y(x² - (3y)²)
= 2x²y(x + 3y)(x- 3y)
Hence, the factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
Learn more about factorization:
https://brainly.com/question/24182713
#SPJ5
A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded. What is the area of the shaded region? (25π – 48) cm2 (25π – 30) cm2 (25π – 24) cm2 (25π – 12) cm2
Answer:
Area of Shaded Region = (25π - 24) cm²
Step-by-step explanation:
See attachment
From the attached, the following observations are made;
Radius, r = 5cm
Base of triangles = 6cm.
Required
Area of shaded region.
If the distance between the base of the triangle to the outline of the circle is 1cm then the height of the triangle is 1cm less than the radius
Height = 5cm - 1cm
Height = 4cm
To calculate the area of the shaded region, we first calculate the area of the circle.
Area = πr²
Substitute 5 for r
Area = π * 5²
Area = π * 25
Area = 25π cm²
Then we calculate the area of both triangles
Area of 1 triangle is calculated as follows.
Area = ½ * base * height
Substitute 4 for height and 6 for base.
Area = ½ * 4 * 6
Area = 2 * 6
Area = 12cm²
Since both triangles are equal.
Area of two triangles = 2 * Area of 1 triangle
Area = 2 * 12cm²
Area = 24cm²
Having calculated the area of the circle and that of both triangles.
Area of shaded region = Area of Circle - Area of Triangles
Area of Shaded Region = 25π cm² - 24 cm²
Area of Shaded Region = (25π - 24) cm²
Answer:
The third one
Step-by-step explanation:
solve system of linear equations by substitution -2x+9y=15
x+7=4
Answer:
1
Step-by-step explanation:
-2x+9y=15
x+7=4
Solve for X.
x +7=4
-7. -7
x = -3
Plug in X into the first equation
-2(-3) + 9y = 15
6 + 9y = 15
-6. -6
9y = 9
Divide by 9 on both sides
9/9=1
Answer:
x = -3. | y = 1. | (-3,1)
Step-by-step explanation:
-2x+9y=15
x+7=4
-7. -7
x= -3
-2(-3) + 9y =15
6 + 9y= 15
-6. -6
9y = 9
÷9. ÷9
y = 1
Suppose that the mean time that visitors stay at a museum is 94.2 minutes with a standard deviation of 15.5 minutes. The standard error of the mean,ox, is 3.1. A random sample of 25 of the times chosen. What interval captures 68% of the means for random samples of 25 scores?
Answer:
[tex] 94.2 -0.994*3.1 = 91.1186[/tex]
[tex] 94.2 +0.994*3.1 = 97.2814[/tex]
And the 68% confidence interval is given by (91.1186, 97.2814)
Step-by-step explanation:
For this case we know that mean time that visitors stay at a museum is given by:
[tex] \bar X = 94.2 [/tex]
The standard deviation is given by:
[tex] s= 15.5[/tex]
And the standard error is given by:
[tex] SE = \frac{s}{\sqrt{n}} =3.1 [/tex]
And we want to interval captures 68% of the means for random samples of 25 scores and for this case the critical value can be founded like this using the normal standard distribution or excel:
[tex] z_{\alpha/2}= \pm 0.994[/tex]
We can find the interval like this:
[tex] \bar X \pm ME[/tex]
And replacing we got:
[tex] 94.2 -0.994*3.1 = 91.1186[/tex]
[tex] 94.2 +0.994*3.1 = 97.2814[/tex]
And the 68% confidence interval is given by (91.1186, 97.2814)
A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14 for Pi.
976.24 mm
976.54 mm
1,852.08 mm
1,953.08 mm
Answer:
4th option: 1953.08 mm
Step-by-step explanation:
circumference of circle= [tex]\pi d[/tex]
Thus, circumference of wheel
[tex] = 3.14(622) \\ = 1953.08mm[/tex]
Answer:
D.
Step-by-step explanation:
Describe two different ways you could change the values in the table so that the answer to problem 6 is different.
Answer:
Um theres no question or picture. Or document.
Step-by-step explanation:
There are ten dogs at the dog park on a busy Saturday. Two of them are Corgis. What is the probability that a randomly selected dog is a Corgi? Type your answer as a fraction in simplest form.
Answer: 1/5
Step-by-step explanation:
From the question, there are ten dogs at the dog park on a busy Saturday and two of the dogs are Corgis. The probability that a randomly selected dog is a Corgi will be the number of Corgis divided by the total number of dogs. This will be:
Probability (Corgi) = Number of Corgis/total number of dogs.
Probability (Corgi) = 2/10
= 1/5
5x – (9x + 14) < 3(x + 10) - 2
Answer:
5x-(9x+14)=−4x−14
3(x+10)-2=3x+28
So, 3(x+10)-2 is greater than 5x-(9x+14)
If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:
Answer:
The correct option is;
[tex]\frac{1}{\pi }[/tex]
Step-by-step explanation:
Here we have that
[tex]Probability = \frac{Number \, of \, required\, outcomes}{Number \, of \, possible\ outcomes} = \frac{Dimension \, of \, the \, line}{Size \, of \, the \ needle} = \frac{l \times D}{\pi \times D \times l } = \frac{1}{\pi }[/tex]
Therefore, the probability that the needle will cut the line = 1/π.
A savings account balance is compounded continuously.If the interest rate is 3.1% per year and the current balance is 1077.00 in how many years will the balance reach 1486.73?
Answer:13.8 is the best answer i could get
Step-by-step explanation:1,077 multiply that × 13.8 =14,862
Sue invested $1,000 at an interest rate of 4% compounded semiannually. How much money
would she have in 3 years?
Answer:
She would have $1,126.16 in 3 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
Invested 1000, which means that [tex]P = 1000[/tex].
Interest of 4%, so [tex]r = 0.04[/tex]
Semianually is twice a year, so [tex]n = 2[/tex]
How much money would she have in 3 years?
This is A(3).
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(3) = 1000(1 + \frac{0.04}{2})^{6} = 1,126.16[/tex]
She would have $1,126.16 in 3 years.
Solve 8.2ws 29.52. Which of the following must be true abo
OWS36
The arrow points left
The arrow points right
There is an open circle at 3.6.
There is a closed circle at 3.6.
Answer:
A B E
Step-by-step explanation:
A- w less-than-or-equal-to 3.6
B- The arrow points left.
E- There is a closed circle at 3.6.
Answer:
A B E
Step-by-step explanation:
I NEED HELP NOWwwwwwww
Answer:
523 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 (3.14) (5)^3
V = 523.33333
Rounding to the nearest whole number
V = 523
Which of the following are geometric series? 2 + 5 + 8 + 11 + 14 + 17 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 –256 + 64 – 16 + 4 – 1
Answer:
-102
Step-by-step explanation:
Answer:
1 and 4
Step-by-step explanation:
Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have earned if her rate is 5.5% compounded annually?
(1) $3159.70 (2) $2936.27 (3) $2942.27
(4) $2925.27
Answer: $2936.27
Step-by-step explanation:
Present value = $1663
Rate = 5.5%
Time(n) = 19years
Future value= PV(1+r)^n
= 1663(1+5.5%)^19
= 1663(1.055)^19
=1663 × 2.766
=4599.86
Interest = Future value - Present value
= $4599 - $1663
= 2936
Geometry Question!!!!
Answer:
D
Step-by-step explanation:
If AB is a tangent, then angle A must be a right angle.
If angle A is a right angle, then triangle ABC is a right triangle and will work in the Pythagorean theorem formula.
a^2 + b^2 = c^2
8^2 + 16^2 = 20^2
64 + 256 = 400
320 = 400
Since 320 = 400 is false, angle A is not a right angle, and AB is not a tangent to circle C.
Answer: D
Solve the equation.
-9x + 1 = -x + 17
X=-8
O X=-2
X = 2
X = 8
Answer:
-9x + x = 17 – 1
8x = 16
X = 16/8
X=2
