The measure of the length GF is 4.2 units and IH is 2.27 units. Then the measure of angle ∠ACB will be 24.35°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle ΔABC and triangle ΔGFC are similar triangles. Then we have
GF / BA = CF / BC
GF / 5.62 = 8.88 / 12.42
GF = 4.018
GF ≅ 4.02
The triangle ΔABC and triangle ΔIHC are similar triangles. Then we have
IH / BA = HC / BC
IH / 5.62 = 5.02 / 12.42
IH = 2.271
IH ≅ 2.27
Then the angle ∠ACB will be
∠ACB = tan⁻¹ (5.62 / 12.42)
∠ACB = tan⁻¹ 0.452
∠ACB = 24.35°
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A researcher wanted to see if different breeds of dogs preferred toys of certain colors. The researcher presented each dog with 3 toys, identical except that each was a different color, and recorded which toy the dog played with the most in a set time period. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
The value for the test statistic and the p value on the test when the researcher wanted to see if different breeds of dogs will be x² = 0.9421 and 0.05 < p value < 0.10.
How to illustrate the research?From the information given, the null hypothesis is that the variables have no difference while the alternative hypothesis is that they have a difference.
The degree of freedom will be:
= (3 - 1) × (3 - 1)
= 4
The critical value is 9.4877. In this case, the p value is greater than the significance level. Therefore, we fail to reject the null hypothesis.
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Answer:
Step-by-step explanation:
From Khan
What is the area of this figure?
Please help
Area of centre rectangle
(8+6+2)(7)(16)(7)112mm²Area of right rectangle
6(3)18mm²Area of triangle
1/2(16-12)(8)4(4)16mm²Total
16+18+112146mm²Let $a_1, a_2, a_3, \dots$ be a non-constant arithmetic sequence. Suppose that $a_4, a_7, a_{12}$ form a geometric sequence. If $a_7 = 30$, what is $a_1$?
The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9
How to determine the value of the first term?The arithmetic sequence is given as:
a₁, a₂ and a₃
The geometric sequence is given as:
a₄, a₇ and a₁₂
The common ratio of a geometric sequence is:
[tex]r = \frac{T_2}{T_1}[/tex]
So,we have:
[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]
Cross multiply
[tex]a_{12} * a_4 = a_7 * a_7[/tex]
Given that a7 = 30, the equation becomes
[tex]a_{12} * a_4 = 30 * 30[/tex]
Evaluate the product
[tex]a_{12} * a_4 = 900[/tex]
Rewrite as:
[tex]a_{4} * a_{12} = 900[/tex]
Express 900 as 10 * 90
[tex]a_{4} * a_{12} = 10 * 90[/tex]
By comparison, we have:
a₄ = 10 and a₁₂ = 90
This means that the geometric sequence is:
10, 30, 90 ---- it has a common ratio of 3
The nth term of a geometric sequence is:
[tex]a_n = ar^{n-1}[/tex]
So, we have:
[tex]a_7 = ar^6[/tex]
[tex]a_4 = ar^3[/tex]
Substitute values for a7 and 14
[tex]ar^6 = 30[/tex]
[tex]ar^4 = 10[/tex]
Divide both equations
[tex]r^2 = 3[/tex]
Take the cube of both sides
[tex]r^6 = 27[/tex]
Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]
[tex]a * 27 = 30[/tex]
Divide both sides by 27
[tex]a = \frac{10}{9}[/tex]
Hence, the value of a1 in the geometric sequence is 10/9
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Find the 58" term of the following arithmetic sequence.
7, 15, 23, 31, …
See the file attached!!
Hope it helps:)
Please help, image below. Thank you!
Answer:
10 Inches
Hope it helps, have a fantastic day.
Step-by-step explanation:
The Circumference of a circle can be displayed by this formula:
[tex]C = 2\pi r[/tex]
[tex]C[/tex] is the circumference, and [tex]r[/tex] is the radius.
So just plug in 31 for [tex]C[/tex], and simplify:
[tex]31 = 2\pi r[/tex]
Because the question is asking for the diameter, we only need to divide both sides by pi, as [tex]2r[/tex] is the same thing as diameter.
[tex]9.87 = 2r[/tex] (rounded to the nearest hundredth)
We can even rewrite [tex]2r[/tex] as [tex]d[/tex], which stands for diameter, to make things a little simpler.
[tex]9.87 = d[/tex]
Now we just take 9.87, and round it to the nearest whole number, and we get 10. So your answer is 10 Inches.
Hope it helps, have a fantastic day.
Aiden has $6,000 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much will he have in 5 years?
Answer:
$7,657.69
Step-by-step explanation:
To find this, use the interest formula:
[tex]A = P(1+r)^{t}[/tex]
A = final amount
P = principal amount ($6,000)
r = interest rate (5% or 0.05)
t = time (5 years)
Given this formula, we can plug in the information and find how much Aiden has after 5 years:
[tex]A = 6000(1+0.05)^{5}[/tex]
[tex]A = 6000(1.05)^{5}[/tex]
[tex]A = 7657.69[/tex]
Therefore, after 5 years Aiden will have $7,657.69.
I hope this helps! Good luck!
Help please
worth 14 points
Answer:
Ok I can walk you through if you comment the questions ok?
Step-by-step explanation:
Trust me :-)
Answer:
1. obtuse
2.straight
3.right
4. acute
5. <EAF
6. <DAF
7. <BAF
8. They are perpendicular to each other
PLEASE HELP IM SO STUCK ON THIS!!!!!
Based on the number of ways to answer the multiple choice questions and the number of ways to answer true or false, the number of ways to answer the test is 8,192 ways.
How many ways can the test be answered?This can be found as:
= Total number of ways to answer multiple choice questions + Total ways to answer true or false questions
Solving gives:
= (4 x 4 x 4) x (2 x2 x2 x 2 x 2 x 2 x 2)
= 64 x 128
= 8,192 ways
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I need help with this problem, Iceman drove at an average speed of 50 mi/h from her home in Seattle to visit her sister in St. Louis. She stayed in St. Louis for 15 hours, and on the trip back averaged 35 mi/h. She returned home 42 hours after leaving. How many miles is Seattle from St. Louis?
To solve this problem, we have to figure out the time spent travelling and then use the speed-distance-time equation to find the distance between the two places. The distance between Seattle and St. Louis is 2295 miles.
How many miles is Seattle from St. LouisTo calculate the miles or distance between Seattle and St. Louis, we have to take into consideration that out of the 42 hours she spent in her journey, she stayed 15 hours over at St. Louis.
[tex]42 - 15 = 27[/tex]
She spent 27 hours travelling.
Her speed in the first journey was 50mi/h and her speed in the second journey was 35mi/h.
This implies she was faster in her first journey compared to her second journey.
Data;
time = 27 hoursspeed = 85mi/h[tex]speed = \frac{distance}{time} \\distance = speed * time[/tex]
Let's substitute the values
[tex]distance = (50 + 35) * 27 = 2295mi[/tex]
The distance between Seattle and St. Louis is 2295 miles
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By cross multiplication find x and y if
ax + by = a² + b² and bx - ay = 0
[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]
x = a and y = b
Step-by-step explanation:
To findThe value of x and y
⠀
Givenax + by = a² + b² (equation 1)
bx - ay = 0 (equation 2)
⠀
Solution{Taking equation 2}
[tex] \sf bx - ay = 0 [/tex]
{Taking ay on RHS}
[tex] \sf bx = ay[/tex]
{Dividing both sides by a}
[tex] \sf \frac{bx}{a} = y(equation \: 3)[/tex]
{Now substituting the equation 3 in equation 1}
[tex] \sf ax + b( \frac{bx}{a} ) = {a}^{2} + {b}^{2} \\ \\ \sf ax + \frac{ {b}^{2} x}{a} = {a}^{2} + {b}^{2} [/tex]
{Taking LCM on LHS}
[tex] \sf \frac{ {a}^{2}x + {b}^{2} x }{a} = {a}^{2} + {b}^{2} \\ \\ \sf \frac{x( {a}^{2} + {b}^{2}) }{a} = ( {a}^{2} + {b}^{2} )[/tex]
{Dividing by (a² + b²) both sides}
[tex] \sf \frac{x}{a} = 1 \\ \\ \green{\boxed {\tt{x = a} } }[/tex]
{Now substituting the value of x in equation 3}
[tex] \sf \frac{ba}{a} = y \\ \\ \green {\boxed{ \tt{y = b}} }[/tex]
Is anyone here like rlly good at algebra bc im not and I kinda forgot What my teacher told me so-
(b + 516= 1000)
I have no clue what to do so-….
Answer:
The question is asking you to subtract 516 from 1,000 to find b.
[tex]1,000 - 516 = 484[/tex]
Therefore, b = 484
Which is the closest to the area that is painted blue? A 308 units B. 116 units C. 463 units? D 124 units
Step-by-step explanation:
first of all, all answer options are basically wrong, because an area is always measured in units² (and not just in units).
the blue colored area is the area of the whole square minus the area of the circle.
the side length of the square is 2 times the radius of the circle (the diameter) : 2×12 = 24 units.
so, the area of the square is
24² = 576 units²
the are of the circle is
pi×r² = pi×12² = 144pi units²
so, the blue area is
576 - 144pi = 123.6106579... ≈ 124 units²
therefore, D is the right answer.
A bag contains 8 black marbles, 16 white marbles, 14 red marbles, and 10 green marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be white? 1/3. 2/3. 3/4. 15/16
Answer:
2/3
Step-by-step explanation:
total marbles is (8 black+ 16 white + 14 red +10 green) = 48
no white cmarbles ( 8+14+10) = 32
32/ 48 = 2/3
32/16= 248/16 =3A square pyramid with a side length of 5 cm and a slant height 7 cm has a total surface area of ... square centimeter
20
165
95
25
70
Answer:
95
Step-by-step explanation:
Surface Area :
⇒ Area (4 triangle faces) + Area (square base)
⇒ 4 x 1/2 x 5 x 7 + (5)²
⇒ 2 x 35 + 25
⇒ 70 + 25
⇒ 95 square centimeters
HELp!!! 100 POINTS.
What is the formula of g in terms of f?
Answer: C
Step-by-step explanation: bcuz
Answer:
[tex]\textsf{A)} \quad f\left(-\dfrac{1}{2}x\right)[/tex]
Step-by-step explanation:
From observation of the given graph, function f has been reflected across the y-axis.
When a graph is reflected across the y-axis, the y-coordinate stays the same while the x-coordinate is negated.
Therefore, replace y = f(x) with y = f(-x), so:
[tex]\implies g(x) = f(-x)[/tex]
It appears that the graph has also been stretched parallel to the x-axis.
When a graph is stretched parallel to the x-axis the x is multiplied by a constant. If the constant is greater than 1, the graph is compressed. If the constant is greater than zero and less than 1, the graph is stretched.
As the graph has been stretched, the constant is 0 < c < 1, so:
[tex]\implies g(x)=f\left(-\dfrac{1}{2}x\right)[/tex]
Find the surface area
Answer:
should be 1305 yd^2
Step-by-step explanation:
to get the surface area of one of the 3 recanglular sides take 24 x 15 to get 360 then muliply by 3 to get 1080 since all the recanglular sides are the same then do 15 x 15 to get both of the triangle sides to get 225 since the equation is 1/2 B x H then add them together
The Hiking Club plans to go camping in a State park where the probability of rain on
any given day is 0.68. What is the probability that it will rain on at least three of the
five days they are there? Round your answer to the nearest thousandth.
Answer:
0.3386 = 0.339 (rounded).
Step-by-step explanation:
It is the binomial type probability distribution.
The number of trial n= 3; the probability of the success trial is 0.16, and the number of success trial k = 1.
Gasoline cost $0.60 a gallon if a car makes 25 miles to the gallon what is will gasoline for an 800 mile trip cost
Answer:
$19.29
Step-by-step explanation:
800 ÷ 25 = 3232 x 0,60 = $19.20there you have it
Which of the following function pairs are inverses?
Answer:
The answer is D.
Step-by-step explanation:
f(x) = 5x -3
y = 5x - 3
Switch y and x to find the inverse
x = 5y - 3
Solve for y.
x + 3 = 5y
y = (x+3)/5
g(x) = (x+3)/5
Pa help po (yung buo sana sagot)
what are you saying?
Step-by-step explanation:
i dont kno if you are a thailander or not???
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?
A composite transformation is the production of the image of a figure through two or more transformation
The set of transformations that could be applied to rectangle ABCD to create rectangle A'B'C'D' is the second option;
Reflected over the y-axis and rotated 180°The reason the above selected option is correct is as follows:
Known parameters:
The given coordinates of the vertices of the preimage of the rectangle ABCD are; A(-4, 2), B(-4, 1), C(-1, 1), and D(-1, 2)
The given coordinates of the vertices of the image of the rectangle ABCD, which is rectangle A'B'C'D' are; A'(-4, -2), B'(-4, -1), C'(-1, -1), and D'(-1, -2)
Solution:
The form of the ordered pair of the vertices of the pre-image is negative value for x, positive value for y, which can be written as (-x, y), where x, and y, are positive numbers
The form of the ordered pair of the vertices of the image is (-x, -y)
The location of a point (-x, y) following a reflection over the y-axis is the point (x, y)
The location of a point (x, y) following a 180° rotation is the point (-x, -y)
Therefore, the set of transformations that can be applied to (-x, y), to create (-x, -y), is a reflection over the y-axis, followed by a rotation of 180
Which gives;
The set of transformations that transforms A(-4, 2) to create A'(-4, -2), B(-4, 1), to create B'(-4, -1), C(-1, 1), to create C'(-1, 1), and D(-1, 2), to create D'(-1, -2) is a reflection over the y-axis followed by a rotation of 180°.Therefore, the correct option is; Reflected over the y-axis and rotated 180°
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Answer: B is your correct answer!
Step-by-step explanation:
What number is 25% of 168?
Answer:
42
Step-by-step explanation:
You turn the percentage into a decimal, 25%=0.25
then you multiply 0.25 to 168
Then you get 42
0.25 x 168 = 42
Hope this helps <3
You send an email with a file size of 4 kilobytes. One kilobyte is 2^{10} bytes. What is the file size of your email in bytes? Write your answer as a power.
Answer:
2¹² Bytes
Step-by-step explanation:
One kilobyte is 2¹⁰ bytes.
File size of the email is 4 kilobytes. That is 4 times 1 kilobyte. Therefore multiply with 4.
4 KB = 4 × 2¹⁰ B
Now notice that you can rewrite 4 like 2².
4 KB = 2² × 2¹⁰ B
Use exponental rule (Product Rule):
[tex]a^x + a^y = a^{x+y}[/tex]
4 KB = 2²⁺¹⁰ B = 2¹² B
Construct an isosceles triangle ABC in which AB=AC = 9 cm and BÂC = 45°. Measure ABC and BC
Answer:
m∠ABC = 67.5°BC = =6.888301782572 cmStep-by-step explanation:
ABC is an isosceles triangle
Then
m∠ABC = m∠ACB
The sum of the interior angles of a triangle is equal to 180°
Then
m∠ABC + m∠ACB + m∠BAC = 180°
Then
m∠ABC + m∠ACB + 45 = 180°
Then
2 × m∠ABC = 180°
Then
m∠ABC = (180−45)÷ 2 = 67.5°
Law of SIN :
[tex]\frac{9}{\sin \left( 67.5\right) } =\frac{BC}{\sin \left( 45\right) }[/tex]
[tex]BC=\frac{9}{\sin \left( 67.5\right) } \times \sin \left( 45\right) ==6.888301782572[/tex]
please help due in 15 mins
Answer:
x is -1
Step-by-step explanation:
-4 multiplied by x is -4x, then -4 x 3 is -12, which makes the problem -4x + -12 and you need to do the opposite so add 4, -4x cancels out and then add 4 to -12 which is 8x
(5x+1)3=15x3 que Propiedad pertenece
Answer:
Step-by-step explanation:
1) Reagrupar términos.
3(5x + 1) = 15x^3
2) Divide ambos lados por tres.
5x + 1 = 5x^3
3) Mueva todos los términos a un lado.
5x + 1 - 5x^3 = 0
4) No se encontró ninguna raíz algebraicamente. Sin embargo, las siguientes raíces se encontraron por métodos numéricos.
x=−0.878886,−0.209148,1.088033
Reason abstractly. A square has vertices at (3,8),(3,2),(9,8), and (9,2). Determine the area.
Answer:
The area is 9 units^2
Step-by-step explanation:
In a bag there are 3 blue marbles, 2 green marbles, 4 red marbles, 1 white marble, and 5 yellow marbles. What is the probability of drawing a green marble then drawing a blue marble from the bag? (With Replacement)
Answer:
So, you must NOT draw a yellow marble on the first draw, a probability of 8/12. Then, you must NOT draw a yellow marble on the second draw, a probability of 7/11. Then you MUST draw a yellow marble on the third draw, a probability of 4/10. So, the three required events, taken together, look like this in lowest terms:
2/3 * 7/11 * 2/5 = 28/165
HOPE IT HELPS!!
A sequence has a common second difference of 4 between terms. The first two terms are 3 and 12. Write down the 3rd and 4th terms.
The first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.
3rd and 4th terms from second level differenceThe 3rd and 4th terms of the sequence is determined from second level difference as shown below;
let the first term = asecond term = bthird term = cfourth term = d(c - b) - (b - a) = 4 ----(1)
(d - c) - (c - b) = 4 ---- (2)
from (1);
(c - 12) - (12 - 3) = 4
(c - 12) - (9) = 4
c - 21 = 4
c = 25
from (2);
(d - 25) - (25 - 12) = 4
d - 38 = 4
d = 42
The sequence = 3, 12, 25, 42
check
first difference = (12 - 3), (25-12), (42-25) = 9, 13, 17
second difference = (13 - 9), (17 - 13) = 4, 4
Thus, the first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.
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Let X and Y be the following sets:
X = {5, 6, 10, 12, 15, 18}
Y = {6, 10, 12, 15)
Which of the following is the set X UY?
Answer:
i think the answer is X, because the elements of both X and Y are in X